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Semantic Networks as Clues: A Theoretical Foundation and Process Optimization for Semantic Network Construction

JinWoo Ha, Dongsoo Kim

Year: 2026Venue: arXiv preprintArea: cs.SIType: PreprintEmbeddings: 235

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Abstract

Abstract:The subject matter of this paper is twofold. One is to review the theoretical foundation of a specific type of Semantic Networks (SNs) representing textual non-propositional knowledge. The other involves proposing a framework (ClueNetwork) for ranking candidate SNs generated through various Semantic Network Construction (SNC) processes for the type. In the first fold, it is clarified that the type serves as clues, not surrogates, of reality, making gold standards elusive. Then, it is discussed why this type nevertheless holds scientific legitimacy in terms of abduction. Grounded in this legitimacy, the three main stages of SNC, comprising Automatic Keyphrase Extraction (AKE), Edge Weighting (EW), and Community Detection (CD), are reviewed alongside their objectives and operations. In the second fold, evaluation criteria (comprising two established and one reformulated) for achieving the objectives are first defined and justified, followed by illustrative experiments based on the criteria. Thereafter, SNC is reformulated as a Process Optimization Problem (POP), and its global objective function that integrates the local criteria is defined and justified. Based on these, ClueNetwork is ultimately proposed.

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Date of publication x 00, 0000, date of current version x 00, 0000. Not Assigned This research was supported by the G–LAMP Program of the National Research Foundation of Korea (NRF) grant funded by the Ministry of Education (No. RS-2025-25441317). Corresponding author: Dongsoo Kim (e-mail: dskim@ssu.ac.kr) Semantic Networks as Clues: A Theoretical Foundation and Process Optimization for Semantic Network Construction JINWOO HA1 AND DONGSOO KIM2 Department of Industrial and Information Systems Engineering, Soongsil University, Seoul 06978, Republic of Korea (e-mail: realfriend@soongsil.ac.kr) Department of Industrial and Information Systems Engineering, Soongsil University, Seoul 06978, Republic of Korea (e-mail: dskim@ssu.ac.kr) Abstract The subject matter of this paper is twofold. One is to review the theoretical foundation of a specific type of Semantic Networks (SNs) representing textual non-propositional knowledge. The other involves proposing a framework (ClueNetwork) for ranking candidate SNs generated through various Semantic Network Construction (SNC) processes for the type. In the first fold, it is clarified that the type serves as clues, not surrogates, of reality, making gold standards elusive. Then, it is discussed why this type nevertheless holds scientific legitimacy in terms of abduction. Grounded in this legitimacy, the three main stages of SNC, comprising Automatic Keyphrase Extraction (AKE), Edge Weighting (EW), and Community Detection (CD), are reviewed alongside their objectives and operations. In the second fold, evaluation criteria (comprising two established and one reformulated) for achieving the objectives are first defined and justified, followed by illustrative experiments based on the criteria. Thereafter, SNC is reformulated as a Process Optimization Problem (POP), and its global objective function that integrates the local criteria is defined and justified. Based on these, ClueNetwork is ultimately proposed. Index Terms: Philosophical considerations, semantic networks, knowledge representation, scientific realism, abduction, exploratory research, distributional hypothesis, percolation theory, Bayesian statistics =-21pt I Introduction Our current subject matter is twofold. One is to review the foundation of Semantic Networks (SNs) as clues, and the other involves proposing a framework to optimize SN Construction (SNC). In this work, SNC is confined to the core phase of SN Analysis (SNA) — the Text Mining (TM) technique comprising data collection and preprocessing, SNC, and post–hoc interpretation of SN representing knowledge [1, 2]. Peers have just encountered key concepts, namely TM, SN, Knowledge Representation (KR), and a network. Text Mining and Semantic Network. Firstly, • TM is a range of techniques for “extracting meaningful information” from textual data [1]. • SN is a network representing knowledge [3, 4]. As may be noticed, a conceptual tension exists between these two definitions. TM extracts information, and SNA is a TM technique. Given that information and knowledge can be defined as “structured data,” and “a mix of information and some ingredient” (e.g., understanding, experience, skills, capability, or values), respectively [5], why is an SN said to represent knowledge rather than information? The answer lies in an interesting observation that while the field of TM tends to regard SNs as “clues” [6] toward true knowledge, the field of KR sometimes regards SNs as “surrogates” [7] of true knowledge. The aforementioned definition of SN reflects reality that discussions of SN itself have been more driven by the KR community that uses specialized SNs, also termed Knowledge Graphs (KGs) [8], as their key instruments, rather than by the TM community, where SNA is merely one of various available tools. Of course, this contrast is made for convenience. We already know that many peers may belong to both communities. For now, it is sufficient to note that, within this paper, SNs are confined to clues. Given that such clues represent knowledge in their own way (Subsection I-A discusses this point in detail), this paper accepts the aforementioned definition of an SN only in a literal sense, not as a surrogate. Knowledge Representation. Likewise, within this paper, the notion of KR differs slightly from the following widely accepted definition within the KR community: • KR is the use of “formal symbols to represent a collection of propositions believed by some putative agent,” or “the field of study concerned with” such uses [9]. Herein, knowledge requires belief. Given that such belief is grounded in an agent’s understanding, experience, or other ingredients, this definition of knowledge partially harmonizes with the aforementioned definition of knowledge (i.e., information ++ some ingredient) [5]. But why “partially?” TABLE I: Key Correspondences between Key Components for SNC. Level Task Role within SNC Objective Evaluation Criterion Input within SNC Output within SNC Local stages AKE Facilitating sparse SN visualization in terms of vertices Keyness hF1hF_1 Textual dataset Document–Term–Matrix EW Facilitating sparse SN visualization in terms of edges Interpretability RI Document-Term-Matrix Raw SN before CD CD Facilitating the capture of local topics inherent in a given textual dataset Distinctiveness Q [21] Raw SN before CD Final SN after CD Global process SNC Providing clues toward true knowledge of a given textual dataset Knowledge representation J Textual dataset Final SN after CD While any proposition can be information111The proposition “this paper has been accepted without revisions” is sadly false, yet it can be informative, indicating that its agent believes a falsehood., any information is not necessarily a proposition. Information is defined as “structured data” [5], yet non–propositionally structured data also exists in the world (Appendix A). This paper selects a specific type of SN that represent textual non–propositional information and knowledge, as opposed to typical KGs. Subsection I-A also discusses this point in detail. For now, it is sufficient to note that, within this paper, KR should not exclude the representation of non-propositional knowledge. Network. Revisiting the definition of KR [9], knowledge can be represented by “formal symbols.” SNC is the process of representing knowledge by constructing a network as a symbolic system, and a network is • a graph–based representation composed of a system’s components and their interactions, which are represented as vertices and their edges, respectively [10]. However, if a network is something represented by such graphical symbols of vertices and edges, why, then, do we not simply call it a graph? Even though a graph as a data structure is necessarily used to construct any network, the system represented possesses its own inherent properties. Because those properties constrain the graph’s topology, it is only then legitimately distinguished as a network, not a mere graph [7]. Network Science. Another noteworthy point is that remarkably diverse systems or phenomena across nature [11], technology [12, 13], and society [14]–[16] have been represented as networks. Consequently, the discovery of principles, which govern specific networks, has been achieved through inductive reasoning [17]: That is, architectures of networks from diverse domains have proven to be similar, and such findings have been elevated to “universal organizing principles” [17] through empirical studies. As a discipline in which such principles, also termed “predictive models” [18], converge, network science has acquired its own universality and has become the foundation for studying networks. Therefore, any network is constrained not only by its system but also by network science. We have also relied heavily on the established percolation theory in network science to facilitate SNC optimization. Subsubsection I-A2 details it. To summarize, our subject matter is about SNC. For a textual dataset, the lower bound of the expectation of SNC is the extraction of meaningful information, and the upper bound is KR. The selected type of SN represents non–propositional knowledge. Such SNs are symbolic systems, governed by universal organizing principles of networks. What, then, does the selected type look like, and how is it constructed? First, it represents keyphrases extracted from a given textual dataset as vertices and weights of semantic relatedness between them as edges. In Subsection I-A, we discuss that this type has trade-offs with the typical type of KG, which represents entities as vertices and their relations as edges. For now, it is sufficient to note that the selected type can be a better choice as a clue rather than a surrogate. Next, when constructing such a clue, three primary stages of Automatic Keyphrase Extraction (AKE), Edge Weighting (EW), and Community Detection (CD) are typically undertaken (Subsections I-B–I-D) [19]. As representing all vertices and edges increases cognitive load during SN interpretation, AKE and EW facilitate SN sparsification by retaining only keyphrases as vertices and only significant interactions as edges [20]. CD also clusters vertices into distinct communities [21, 22], thereby capturing local topics. Corresponding to these roles, the stages aim to achieve respective objectives of keyness, interpretability, and distinctiveness. The degrees of belief in achieving these objectives can also be measured, and hF1hF_1, percolation–theory–based RI, and a community scoring function [21] are used as those criteria in this paper. Subsections I-B–I-D clarify the definitions of these stages and objectives, and Subsection I-A justifies the choices of the criteria. For now, it is sufficient to note the correspondences of these components (Table I). Beyond reviewing these components, our final aim is to propose a framework to optimize SNC. What, then, is the background of this proposal? It is as follows: AKE, semantic relatedness estimation (referred to as edge weighting within this paper), and community detection are research areas that can independently exist even outside SNC. As to be reviewed in Subsections I-B–I-D and I-A, each area encompasses available methods and evaluation protocols. So, any researcher conducting SNC should systematically select an appropriate method from a rich set of alternatives at each stage. However, many applications still rely on a limited number of conventional pipelines222They typically involve Term Frequency (TF) or TF–IDF [23] for AKE, Co–occurrence Frequency (CF) for EW, and the Clauset–Newman–Moore (CNM) [24] or Louvain [25] algorithms for CD. [19]. Whether SNs constructed in such manners guarantee optimal outcomes remains an unaddressed question. This limitation stems from the fact that while evaluating methods within each stage is straightforward, ranking resulting SNs in an integrative context remains challenging. Against this backdrop, Subsection IV-B presents our SNC framework facilitating such ranking. What, then, is the criterion for determining that one SN is more reliable than another? Crucially, our notion of an optimal SN is distinct from some external gold standard assumed in KG refinement or KG alignment. Rather, the notion aligns with some SN that achieves the highest joint confidence for the local objectives (i.e., keyness, interpretability, and distinctiveness), given available method combinations across the stages. Figure 1: SNC Depicted as a Brick–Stacking Problem. Optimal construction is achieved through the systematic selection and combination of bricks. Likewise, SNC requires the systematic selection and integration of methods. This illustration is inspired by the BERTopic documentation (link). Within this paper, such confidence is measurably defined as a global objective function J. Subsection IV-C justifies its form. For now, it is sufficient to refer to Fig. 1 illustrating the simplified version of our framework ClueNetwork (its full version is detailed in Subsection IV-B). Herein, SNC is depicted as a Process — also can be termed a pipeline, policy, or brick–stacking — Optimization Problem (POP): First, choices of local methods should be evidence–based. At each stage, candidate methods are evaluated by using a stage–specific criterion. Next, the gathered evaluation results are integrated into J. Finally, some optimal combination of methods that maximizes J is identified for a textual dataset. This paper contributes to the body of knowledge in reaching the framework as follows: Theoretical Foundation. Section I addresses the following Research Questions (RQs) to ensure a theoretical foundation for SNs as clues: How does the selected type of SN represent knowledge (RQ1)? When is the type, rather than typical KGs, recommended to be constructed (RQ2)? What are the definitions of the SNC stages and their objectives (RQ3)? Which stage–specific methods have been selected for the Proof of Concept (PoC) of ClueNetwork (RQ4)? Empirical Record. Section I holds value as an empirical record. By providing illustrative experiments, which stage–specific selected methods yield high performance (RQ6) is presented. Before it, the section answers how the local evaluation criteria (hF1hF_1, RI, and Q) are defined and justified (RQ5). ClueNetwork. In response to how evaluation results across the SNC stages are integrated to identify the optimal SN (RQ7), Section IV presents our framework ClueNetwork. Crucially, it facilitates ranking candidate SNs for a textual dataset. The section also answers how ClueNetwork’s objective function J is defined and justified (RQ8). ClueNetwork is more than integrative, as it incorporates two innovative methodological components, namely RI and a veracity pretest for edge weighting measures. They are built upon the established percolation theory and the Matthews correlation coefficient [26], respectively, yet with a touch of novelty. Finally, only after Section V carefully discusses not only such contributions but also ClueNetwork’s limitations does Section VI conclude this paper. I Theoretical Foundation This review section comprises four subsections. Subsection I-A first reviews several philosophical topics to distinguish the selected type of SN from typical KGs, thereby addressing RQs 1 and 2. Next, Subsections I-B through I-D review the SNC stages along with their respective objectives and considerations. Each subsection also summarizes the philosophies of selected methods that optimize the corresponding local objective. Thereby, Subsections I-B through I-D themselves serve as the answers to RQs 3 and 4. Before that, we would like to clarify that collecting or granular clustering as many local methods as possible is beyond our scope. We only need some materials for the PoC of ClueNetwork. Accordingly, we have selected relatively accessible and implementable local methods and have provided a simplified (not granular) taxonomy of methods for each SNC stage. Instead, we have cited some specialized review papers focusing on granular clustering for interested readers. TABLE I: Four Central Theses, Formulated by [28], of Scientific Realism. No. Core Stance Full Principle Thesis 1 Confidence for the correspondence between scientific terms and reality Even when scientific theories mention unobservable terms (e.g., dark matter), such terms should be regarded as referring to real things. Thesis 2 Confidence for the verifiability of whether scientific theories align with reality As scientific theories are frequently “confirmed as approximately true by ordinary scientific evidence,” interpreted based on “methodological standards” [28], they are verifiable. Thesis 3 Confidence for scientific progress Science progresses largely through “successively more accurate approximations to the truth” [28]. That is, later scientific theories are established largely “by standing on the shoulders of giants” [29] (i.e., “the knowledge embodied in previous” scientific theories [28]). Thesis 4 Confidence for the independence of reality Reality exists regardless of whether scientific theories aiming to explain it are true or false. That is, reality remains “largely independent of our thoughts or theoretical commitments” [28]. I-A Surrogates and Clues To begin with, there is a straightforward fact. If any type of SN aims at KR, who constructs them most actively? Certainly, scientists (including engineers who consider scientific principles). Science is, by its very nature, an activity dedicated to true knowledge. Indeed, it is defined as • “the organized and systematic enterprise that gathers knowledge about the world and condenses the knowledge into testable laws and principles” [27]. Hence, if we can comprehend scientists’ common sense, we may be able to recommend appropriate types of SNs for them. Let us consider the following. Scientific Realism [28] is a doctrine embodying the theses presented in Table I. According to them, reality exists independently of human minds (Thesis 4), scientific theories (sets of “testable laws and principles” [27]) correspond to reality (Thesis 1), and such correspondences are verifiable (Thesis 2). Scientific realism aligns with the common sense of most scientists. For example, this journal IEEE Access asks reviewers, “Does the paper contribute to the body of knowledge?” It presupposes that such a body independently exists and that reviewers can verify whether submissions contribute to it. Reality. Throughout those theses, reality serves as an independent criterion to verify knowledge. What, then, is reality? • Reality is the domain of “that which there is. (…) How much of it there is forms the subject of ontology” [30]. Here, one might ask, “Wait, we already encounter everyday beings. Why, then, should we single out reality?” For most philosophers, existence is far from a trivial condition. For instance, Plato, one of the earlier realists who deeply contemplated reality, believed that only fixed (constant, uniform, and immutable) things purely exist [31]. Plato referred to such things as “the Forms” [31]–[34]. Whether we agree with Plato’s claim or not, it warrants consideration. In a corner of our laboratory, a banana is rolling around, seemingly in existence. If we ignore it for two months while focusing on this re–revision, will it still be a banana? It is likely to become some horrific organic matter, not a banana anymore. Most everyday things are not fixed. Plato referred to such transient things as “rolling around between what is not and what purely is” [32]. Numerous philosophers have spent the last 2,400 years debating what belongs to reality. The Forms and Gold Standards. Apart from that debate, why is reality desired as an independent criterion of knowledge? To scientists, transient things remain too uncertain to serve as criteria. Claiming that their knowledge is true based on the knowledge itself could be circular reasoning. If there is something that exists fixedly and independently, it becomes far easier to say, “Look! My knowledge harmonizes with reality, so it is true.” Interestingly, a similar approach is observed in KG refinement and KG alignment, often performed by knowledge engineers. Herein, • KG refinement consists of KG completion and KG error detection; the former is the task of “adding missing knowledge” to a KG, and the latter is the task of “identifying and removing errors” in a KG [35]. • KG alignment, also termed entity alignment, is “the task of finding” [36] and “linking entities sharing the same identity” [37] across multiple KGs. The concerns of KG refinement and KG alignment are whether KGs are complete and correct [35] and whether KGs are properly integrated [37], respectively. To address these concerns, knowledge engineers rely largely on independent criteria333For example, KGs deemed to possess higher qualities than target KGs, common knowledge bases (e.g., Wikidata [38]), or domain experts. termed “gold standards” [35, 39], subsets of which are sometimes classified as “partial gold standards,” “silver standards,” or “human (post–hoc) judgment” [35] depending on their qualities or formats. Does this setup look familiar? Figure 2: The Physical Review’s decision is confirmable through records, whereas the meaning of (Square, 0.90.9, Circle) cannot be queried to Yi Sang. Yes, it is Plato again. He believed that the reason an everyday thing seems somehow beautiful is that it partially shares the Form of Beauty [31]. Likewise, the reason a KG is deemed to represent true knowledge partially is that the KG partially reflects a gold standard. Plato believed that as the Forms are fixedly being, contemplating them is to gain true knowledge [32, 33]. Similarly, as gold standards are fixed, comparing them to KGs is deemed to determine the veracity of the KGs. Surrogates and Propositions. As such, whether welcome news or not, the Platonic way of thinking somehow resembles the way KGs operate. To many peers, KGs are something that, by approximating true knowledge, ultimately become its “surrogates” [7]. What are such KGs likely to be composed of to make it easier to verify them? Certainly, propositions, as they are “declarative sentences, believed by some putative agent, that can be true or false, right or wrong” [9]. Indeed, typical KGs consist of subject–predicate–object structures, also termed triplets, that can be intuitively transformed into propositions. Let us suppose there is a KG of physics (Fig. 2–a). It can include the triplet (Physical Review, requested a revision, Einstein), from which “some putative agent” [9] (we) can easily infer that the triplet represents the proposition, “The Physical Review requested a revision from A. Einstein.” And it is very confirmable (Fig. 2–b), because the historical records of the review process exist [40]. Likewise, when [8] defined a KG as “a graph of data intended to accumulate” and represent knowledge, many peers likely regarded such knowledge as “a collection of propositions” [9]. And there are reasons. With the resurgence of AI over the past few decades, studies leveraging KGs as references used by AI–based systems to achieve something innovative are increasing. Given that such systems often exhibit a black–box nature, making even their references something whose “true or false, right or wrong” [9] and meanings are ambiguous might amount to opening Pandora’s box. To many peers, KGs should be “surrogates” [7] that reduce room for variances from AI–based systems. Case of Square Circle. However, humanity has taken on the role of “some putative agent” [9] long before AI. Let us suppose an instance of the selected SN type regarding the poetry of Yi Sang, who is a Korean writer. Although the SN (Fig. 2–c) can include the triad (Square, 0.90.9, Circle), because 0.90.9 is not a predicate, the triad cannot be immediately converted into a proposition. Only through circuitous reasoning do we say, “The triad implies that the collocation of square and circle occurs in the dataset with a degree of 0.90.9,” yet the triad itself does not represent any proposition. This derivation requires intervention from the agent (us), as the collocation is far from everyday contexts. In fact, the square circle refers to a revolving door of a department store (Fig. 3), given that our literature teachers taught us so. The teaching was possible because Yi Sang researchers had reached a consensus based on several clues. Specifically, Yi Sang was an architect; the objects in the poem (link) resemble the features of the department store (link); the title is “At the Department Store” [42]. However, these are not Yi Sang himself. He returned to stars in 1937 (Fig. 2–b). That is, in certain cases, reaching gold standards is extremely difficult. Far more datasets than expected are context–dependent, trendy, or too large in volume to be read. Their gold standards are largely not yet ready. As many researchers cannot afford to wait for such criteria, they strive to produce possible explanations at the moment by adding their expertise–based beliefs as ingredients to available clues. Whether true or not, such explanations harmonize with the definition of knowledge (information ++ some ingredient) by [5]. The attitude of pursuing more coherent explanations also aligns with Thesis 33 reserved until now of scientific realism (Table I). As long as such explanations are under researchers’ responsibility, there is no reason to exclude the explanations from the domain of knowledge. Semantic Networks as Clues. Then, can (Square, 0.90.9, Circle) itself be considered knowledge? Yes, it can. First, as it is “structured data” [5], it qualifies at least as information. Second, it is also knowledge, given that this structuring was only possible because Yi Sang’s belief — that the revolving door resembles the square circle — had been embedded within the data. Third, as discussed in Subsections I-B through I-D, the triad already reflects the beliefs of particular AKE and EW algorithms regarding which phrases are representative and worthy of being connected. In short, some data producers, some local SNC algorithms, and some interpreters are all “some putative agents” [9]. Given that beliefs intervene at least at the SNC phase444Certain data might be mere noise. And even if an SN is constructed, it might be left uninterpreted. However, without SNC, the SN cannot exist. among the three stages (production, SNC, and interpretation), triads of the selected type of SN should be considered to represent knowledge. Therefore, we are now ready to answer RQ1 (“How does the selected type represent knowledge?”). Based on information constructors’ beliefs (i.e., local SNC algorithms’ philosophies), it represents knowledge by implying data producers’ beliefs as non–propositional triads. To convert such triads into propositions, interpreters intervene only after SNC. As a system of such triads, the selected type can be considered as a clue, in that it can serve as the starting point for interpreters to derive hypotheses (propositions not verified yet) regarding what is implied. Although their KR ways differ, both the selected type and typical KGs belong to the SN family, as they do KR [3, 4]. They merely diverged in the late 1980s when some researchers in the Netherlands designed a type of SN characterized by “a limited set of relations” [43], as KGs. To avoid confusion and for brevity, the selected type and typical KGs are hereafter referred to as SNs and KGs, respectively. Abduction and Exploratory Research. Here, one might ask, “Okay, SNs do KR. However, if such knowledge cannot be compared to some gold standards, would it not violate Thesis 2 and thus fail to qualify as scientific knowledge?” It does not. First, Thesis 2 (Table I) simply states that “methodological standards” [28] should be used for scientific verification. It does not restrict them to gold standards. Second, although such methodological standards vary, they are fundamentally certain combinations of deduction, induction, and abduction, termed “the three types of reasoning” [44]. Figure 3: Yi Sang likely envisioned the square circle upon seeing a revolving door. This figure was generated by using [41]. As presented in Table I and according to [44], deduction is the reasoning that “proves that something must be” by deriving “necessary consequences” from given propositions; induction is the reasoning that determines the actual degree to which something operates through observations; abduction is the only reasoning that “forms an explanatory hypothesis” that “suggests that something may be.” TABLE I: Examples of Deduction, Induction, and Abduction. This table is secondarily cited from [45], and the examples have been altered by us. Deduction Induction Abduction Rule: All PhDs in this lab get grants. Case: These PhDs are in this lab. Rule: All PhDs in this lab get grants. Case: These PhDs are in this lab. Result: These PhDs get grants. Result: These PhDs get grants. Result: These PhDs get grants. Rule: All PhDs in this lab get grants. Case: These PhDs are in this lab. Each cell in the final row represents a derived proposition. Most gold–standard–based KG evaluations are certain combinations of deduction and induction. A typical combination for arbitrary propositions a,b,c, and da,b,c, and d is as follows, where the propositions shared by both reasonings are presented without parenthetical annotations: • Rule (Deduction): The gold standard says a,b,c, and da,b,c, and d. • Case: The KG claims ¬a,b,c, and ¬d a,b,c, and d. • Result: The KG yields false, true, true, and false for a,b,c, and da,b,c, and d, respectively. • Rule (Induction): The KG’s F1F_1 score is 0.670.67. Herein, interestingly, knowledge engineers (i.e., modern scientists) do not insist on deduction. However, Plato regarded deduction as the superior intellectual activity [33]. That is, while science operates similarly to the Platonic way in some aspects, it is obviously not always the case. Scientists also legitimately and frequently employ certain combinations of abduction and induction. For example, [46] derived a hypothesis through SNA–based abduction that Reddit555Reddit is a well-known social media platform. r/Republican and r/democrats are its subreddits (discussion forums). users with different political orientations share views on which events and politicians warrant discussion: • Rule: Submissions from r/Republican and r/democrats share linguistic patterns when sharing views on what warrants discussion. • Result (Abduction): Wow! Collected submissions from r/Republican and r/democrats share linguistic patterns. • Case: The collected submissions share views on what warrants discussion. • Result (Induction): The differences between the scores of words in the collected submissions are not statistically significant. • Rule: The submissions from r/Republican and r/democrats share linguistic patterns when sharing views on what warrants discussion. Herein, [46] only performed their work up to the hypothesis (Case) generation level. Nevertheless, it was legitimately published in a scientific journal, because the generated hypothesis can be tested through induction at any time, thereby providing a new starting point for research. Such abduction originates from a wow moment when a researcher encounters a “surprising fact” [47], leading to a hypothesis by filtering that fact through the researcher’s existing belief (Rule). That is, science progresses not only through gold standards or hypothesis testing, but also through such exploratory research [48]. Knowledge reserved for verification is not equivalent to unverifiable knowledge. Even Yi Sang’s square circle cannot be definitively assumed to remain indefinitely as literary knowledge rather than scientific knowledge, as his undiscovered diaries might come to light someday. Accordingly, we are now ready to answer RQ2 (“When are SNs, rather than KGs, recommended to be constructed?”): In works requiring verification–oriented KR, KGs are superior to SNs. Conversely, SNs are recommended for works focused on hypothesis–generation–oriented KR or where gold standards are lacking. While KGs should be employed in works requiring propositions for AI, SNs can be considered when researchers need the power of open interpretation to move beyond predefined propositions. As such, there are simply trade–offs between KGs and SNs. I-B Automatic Keyphrase Extraction In the previous subsection, we reviewed the philosophical foundation of SNs. Now, we can transition to the review of the individual stages required for constructing such SNs. This subsection is the first of Subsections I-B through I-D, which themselves constitute the comprehensive answers to RQ3 (“What are the definitions of the SNC stages and their objectives?”) and RQ4 (“Which stage–specific methods have been selected for the PoC of ClueNetwork?”). I-B1 What is AKE, and Why Does It Matter? Keyphrase Extraction (KE) is “a fundamental subtask of Natural Language Processing (NLP)” [49], and also frequently serves as an important subtask across diverse applications of Text Mining (TM) and Information Retrieval (IR) [50]. According to [50] and [51], KE is defined as • the automatic extraction of phrases that “best represent” [50] or “concisely summarize” [51] a document. As shown above, relevant papers (e.g., [52]–[56]) often emphasize that KE is performed automatically, thereby also referring to KE as Automatic KE (AKE). Why? Given that the volume of available documents today typically exceeds what users can thoroughly read and analyze, KE as an automatic rather than manual subtask is feasible [50]. Meanwhile, in the above definition, a phrase refers to a textual unit composed of one or more tokens [49, 50]. As a phrase is distinguished from larger textual units (e.g., documents, paragraphs, or sentences), it is also referred to as a “lexical unit” [51] or simply a “term” [49]. Keyness. From the definition of AKE, we can also deduce the definition of keyness. Since keyphrases have already been defined as “phrases that best represent or concisely summarize a document,” the property described by this relative clause is precisely what constitutes keyness in terms of AKE: • Keyness is the property whereby a document is “best represented” [50] or “concisely summarized” [51]. Phrases possessing this property are legitimately prefixed with key–. However, according to [50], keyness is linked to at least ten different properties (for which please see [50]), rendering further specification of its meaning “elusive.” Considering its scope and for brevity, this paper certainly does not undertake that work. Instead, Subsubsection I-B2 reviews different philosophies of keyness embedded within the selected AKE algorithms, in light of the observation by [50] that interpretations of keyness are application–dependent. Necessity in SNC. AKE is also essential in SNC because no SN can be constructed without vertices. One might ask, “Okay, but why should SNs represent keyphrases as vertices? KGs represent entities without any problems.” A KG is graph–structured data intended to accumulate and represent knowledge, whose vertices and edges are “entities of interest” and their relations [8]. Herein, any KG assumes an interest, whereas, given that an SN is directly extracted from a textual dataset, entities of specific interest are largely not predefined. That is, KGs represent knowledge of specialized interests [8], whereas SNs represent knowledge of texts [2]. In terms of SNC, what matters is not which vertices accurately represent an interest, but rather which vertices “best represent” [50] texts. This is why keyphrases are employed as vertices, and AKE serves as an irreplaceable stage in SNC. Maximization of Keyness. Ultimately, the objective of AKE is to comprehensively extract phrases that possess keyness for a document. Within this paper, this objective is termed “the maximization of keyness.” Such maximization is specifically and typically regarded as maximizing the alignment of a set of extracted phrases with the “golden set of keyphrases” [49]. The actual degree of such alignment can also be quantified and evaluated by using a specific criterion (e.g., F1F_1, pF1pF_1, or hF1hF_1) as explained in Subsection I-A1. Scientific Realism Revisited. As may be noticed, while ClueNetwork does not assume the existence of a gold SN for a textual dataset, AKE assumes that of gold keyphrases. That is, by reflecting Theses 1, 2, and 4 (Table I), AKE serves as an anchor rendering ClueNetwork scientifically realistic. This reflection is feasible, given that constructing sets of gold keyphrases is easier than constructing a gold SN (Subsubsection IV-B2). Furthermore, the definition of a clue is “a piece of evidence leading to discovery” [57]. To scientists, discovery often signifies finding true knowledge consistent with reality. Accordingly, technologically sound AKE should enable the clues (SNs) to encompass some pieces of reality. I-B2 How Does AKE Work? Beliefs as Ingredients. AKE typically operates in a manner where an AKE algorithm x formulates a proposition, such as “The keyness scores of candidate phrases a,b,ca,b,c, and the rest for a document d are 1.0,0.9,0.81.0,0.9,0.8, and below, respectively,” based on its belief (interpretation of keyness). Herein, the definition of a belief is a judgment that “the world is one way and not another” [9]. That is, x judges the world to be one where a,b, and ca,b, and c possess higher keyness. Ranking Candidates. As may be noticed, ranking candidates is central to AKE, given that their priorities ultimately matter. Here, a relevant consideration arises. Some AKE algorithms use lower–is–better scoring (e.g., [58] and [59]), and their resulting scores often follow skewed distributions that can complicate data analysis. Hence, ClueNetworkClueNetwork normalizes candidate scores to a 0 to 11 scale under the higher–is–better convention. Specifically, (1)–a is applied to original higher–is–better scores, and (1)–b to original lower–is–better scores. r−rmin+ϵrmax−rmin+2ϵ⋯(a)rmax−r+ϵrmax−rmin+2ϵ⋯(b) (1) Herein, for a document, r is the rank of a candidate’s score (higher rank numbers indicate higher original scores); rmaxr_max and rminr_min are the maximum and minimum ranks, respectively; ϵ=10−8ε=10^-8 is a small constant handling corner cases where only tied candidates exist (i.e., rmax=rminr_max=r_min). Construction of 2–mode Matrix. In terms of SNC, although each term’s final score is required to represent only keyphrases across a dataset as vertices [20], AKE is typically performed on respective documents [49]. Hence, to facilitate computing each term’s final score by aggregating its normalized individual scores, a 2–mode matrix is constructed, with rows, columns, and cells corresponding to windows, terms, and scores, respectively. Herein, a window is a textual range (e.g., document, paragraph, sentence, or n–gram) depending on the purpose, but it is typically set to a document. That is, in SNC, as a result of document–wise AKE, an initial Document–Term Matrix (∈ℝm×nDTM ^m× n) is typically built, where m and n are the numbers of documents and terms, respectively. Herein, Score(ti, h)Score(t_i, h) is the normalized score of the iith term tit_i for the hhth document, and the term’s final score is obtained by summing its normalized individual scores: Final Score(ti)=∑h=1mScore(ti, h)=∑h=1mh, iFinal Score(t_i)= _h=1^mScore(t_i, h)= _h=1^mDTM_h, i (2) Simplified Taxonomy of Unsupervised Algorithms. What algorithms exist to score terms under respective philosophies of keyness? Numerous relevant algorithms (e.g., [52]–[56] and [58]–[83]) have been proposed with benchmarking (i.e., gold–standard–based) experiments [49, 51]. According to [51], such algorithms can be categorized as supervised or unsupervised ones. As the latter, which requires no training data, is more widely employed, this paper focuses on it. It can be further categorized as follows [49, 51]: Figure 4: Simplified Taxonomy of Unsupervised AKE Algorithms. First, statistics–based algorithms exploit statistical features of textual units (e.g., [23], [55], [58], [60], and [61]). For instance, TF and TF–IDF [23] regard a higher frequency of a term as a necessary condition for keyness. Their successors, such as KP–Miner [61] and YAKE! [58], also incorporate other features, such as positional or linguistic ones. Second, graph–based algorithms exploit a graph, which represents textual units as vertices and their interactions as edges, inherent in a document (e.g., [52]–[54] and [62]–[76]). Interestingly, these algorithms remind us that graphs are prevalent in the world (Section I), as they fundamentally view influential vertices as possessing keyness. Third, Neural–Network–based (N–based) algorithms explicitly execute neural models to capture contextual semantics of a document. Although their frameworks and philosophies of keyness diverge (e.g., [54], [75], [77], and [78]), two prominent trends are observed. One trend (e.g., [59] and [79]–[81]) is to compute similarity scores between vector representations (also termed embeddings), extracted by a Pretrained Language Model (PLM), of a document and those of candidate phrases. The other (e.g., [82] and [83]) is to extract keyphrases by feeding a document and an appropriate prompt into a PLM or a Large Language Model (LLM). Fourth, most AKE algorithms are somewhat hybrid or idiosyncratic. Can a graph–based algorithm leveraging a PLM also be N–based (e.g., [75])? If an algorithm does not execute a neural network but references third–party static word embeddings, can it be N–based (e.g., [65] and [69])? Are alternative categories required for algorithms that obtain word embeddings through matrix factorization (e.g., [84]) or leverage clustering (e.g., [60]) or game theory (e.g., [56])? These corner cases illustrate that the boundaries between the three main categories are often blurred. Hence, Fig. 4 should be regarded as a convenient abstraction. Readers interested in a more meticulous classification may consult [51], an AKE–specialized review paper. For insights into relatively recent trends, readers may also consult [49]. Readers interested in specific frameworks or parameters of the selected AKE algorithms may consult the original references. For brevity, the following paragraphs provide only high–level summaries of the algorithms selected based on whether they significantly reflect their category characteristics, whether their Python implementations are available, and whether their reported performances are competitive [49, 51], [81, 82], [85, 86]. Parameters associated with specific descriptions of the algorithms have been denoted within parentheses with distinct symbols, abbreviated as “pa.”: • For instance, “KP–Miner boosts IDF (pa. σ and α).” Term Frequency (TF) and TF–Inverse Document Frequency (TF–IDF). TF is solely concerned with how many times a term occurs in a document. That is, TF regards a higher frequency of a term as a necessary and sufficient condition for keyness. Given that using only TF may extract common terms that cannot represent local topics in a document, TF–IDF [23] incorporates Inverse Document Frequency (IDF) to counterbalance TF. IDF penalizes common terms and compensates for terms that are rare across a textual dataset yet frequently occur within certain subsets of the dataset. The philosophy underlying TF–IDF is to view both TF and IDF as the necessary conditions for keyness. KP–Miner [61] introduces four improvements to TF–IDF. First, for a document, KP–Miner does not regard certain terms as candidates if they occur fewer times than a specified “least allowable seen frequency (pa. lasf)” [61], or first occur after a specified number of words (pa. cutoff). Second, KP–Miner prevents the underestimation of multigram terms. Third, it boosts IDF (pa. σ and α). Fourth, it weights terms that first occur in early positions (pa. PfP_f). In short, KP–Miner believes not only unigrams but also multigrams possess keyness if they occur above a threshold at the beginning of a document, where key information can be concentrated. YAKE! [58] rewards a term when it occurs more frequently than average, in many sentences, in early sentences, or in capitalized forms. Conversely, YAKE! penalizes a term when its left [right] neighbors are diverse, indicating a higher likelihood of being a common term (pa. window), or when its unigrams do not form a meaningful multigram but rather end or begin with a stopword (e.g., “doctor of” instead of “doctor of philosophy”). Given that YAKE! collects all these features, it marks a singularity that statistics–based AKE algorithms encountered limitations in adhering to frequentism. Selected Graph–based Algorithms. TextRank [62], a pioneer of graph–based algorithms, builds a graph representing lexical units as vertices. The graph links two vertices if they co–occur in at least one sliding window frame666Given a document “GPUs go brrr” and a specified window size of 22, the sliding window frames are “[GPUs go] brrr” and “GPUs [go brrr].” (pa. window). Then, TextRank runs PageRank [87] that recursively updates each vertex’s score until it converges (pa. δ). PageRank rewards a vertex if it has many edges or is linked to such influential vertices. Only vertices whose final scores rank in the top T percent are retained (pa. T). Each candidate’s score is determined by summing its constituent vertices’ scores. SingleRank [63] resembles TextRank but differs in that edge weights are determined by co–occurrence frequencies of lexical units across sliding window frames rather than being binary. PositionRank [71] also resembles SingleRank but differs in that PositionRank rewards a vertex if it occurs in early positions in a document. In short, all three algorithms believe influential terms possess keyness, but SingleRank and PositionRank believe such terms are frequently co–occurring terms. PositionRank further believes such terms should occur at the beginning of a document. Selected N–based Algorithms. Firstly, KeyBERT (Fig. 5) [80] is a very simple N–based algorithm. Figure 5: Overall Workflow of KeyBERT. It feeds a document and corresponding candidate terms into a PLM, thereby obtaining a document embedding and candidate embeddings. Then, it computes the cosine similarity between the document embedding and each candidate embedding, selecting candidates with the highest similarity values as keyphrases. “BERT” [88] in KeyBERT’s name is not necessary. While a lightweight BERT variant is typically employed as a PLM backbone in KeyBERT, a recent State–Of–The–Art (SOTA) model such as harrier–oss–v1–27b [89] can also be employed, provided that a high–end GPU is available. In contrast, MDERank (Fig. 6) [59] believes direct similarity computation between a document and each candidate isolates candidates from the document’s full context. Hence, MDERank computes the similarity between the embedding of the original document and each embedding of a masked version of the document, in which the corresponding candidate is masked with the special token [MASK]. Here, MDERank uses lower–is–better scoring, given that if a candidate is a keyphrase and its masking causes a significant loss of the full context, the similarity score decreases. Figure 6: Overall Workflow of MDERank. Meanwhile, LMRank [81] resembles KeyBERT but differs in several aspects. First, LMRank avoids employing a BERT variant, typically pretrained through Masked Language Modeling (MLM) [88]. Instead, LMRank employs MPNet [90] as an alternative PLM backbone. MLM can learn positional information of tokens, but fails to capture dependencies between masked tokens [88, 90]. Hence, MPNet believes a BERT variant struggles to adapt when encountering a complex textual context [90]. Second, although MPNet has a shorter input limit of 384 tokens [90] compared with the typical 512–token limit of BERT variants [88], LMRank circumvents this constraint by segmenting a long document and computing its final embedding through average pooling. Third, LMRank runs meticulous preprocessing to select appropriate candidates, such as syntactic dependency parsing between terms, removing trivial terms, restricting candidates to noun phrases (pa. keeps_noun_adjskeeps\_noun\_adjs), and handling overlapping terms by retaining only the most representative ones (pa. deduplicatededuplicate). Fourth, LMRank can also boost similarity scores of candidates that occur in early positions in a document (pa. positional_featurepositional\_feature and μ). In short, these N–based algorithms believe terms closely aligned with their document’s context within a high–dimensional embedding space possess keyness. I-C Edge Weighting I-C1 What is EW, and Why Does It Matter? Edge Weighting (EW). We now suggest that peers approach EW, employed as the second stage in SNC, without considering its definition too abstractly. It literally refers to assigning specific weights to edges while constructing a network. Depending on what kind of system a network represents, an edge weight can signify, for instance, “the average number of interactions per day” [15] between two employees in a workplace, or “the number of meetings that two individuals jointly attended” [16]. In SNC, an edge weight is confined to semantic relatedness between two keyphrases (vertices). Semantic Relatedness is defined as a human–perceivable connection between two concepts [91, 92]. Herein, concepts subtly differ from words (terms)777In the field of NLP, terms, words, phrases, and lexical units often have blurry boundaries. This paper also uses them interchangeably.. Concepts refer to word senses, and a word (e.g., doctor) can convey different word senses (e.g., doctor as a Ph.D. versus a medical doctor) depending on semantic context (e.g., academic versus medical) [93]–[95]. According to [92, 93], humans can perceive two words (ultimately, two concepts) as connected if there exists at least one semantic or mere lexical relation between them, as detailed in Appendix B. When such relations are somehow typed, they are termed “explicit” [92, 94, 95] relations. Semantic similarity also exists, but it is a mere special aspect of semantic relatedness [91], [94]–[97]. Criteria for distinguishing them are presented in Appendix B. More relevantly, semantic relatedness can be measured as a weight between 0 and 11, depending on the perceived degree of such a connection [95]. Here, semantic relatedness is also regarded as the opposite of semantic distance [91, 93, 96, 97]. In short, EW in SNC is equated to measuring (estimating) semantic relatedness weights between extracted keyphrases. Indeed, semantic relatedness is also defined as “how much connection humans perceive between two concepts” [91]. Hereafter, it is referred to as relatedness. Necessity in SNC. A structure where only unlinked keyphrases float is a mere word cloud. Edges are essential to form a meaningful SN. However, even an SN representing only 5050 vertices can represent up to (502)=1,225 502=1,225 edges. Representing all such edges imposes an excessive cognitive load on an interpreter. Hence, only significant edges can be retained by omitting or visually thinning zero– or low–weighted relatedness [2, 20]. Given that EW provides the criteria for such SN sparsification, it is necessary in SNC. Maximization of Interpretability. Seemingly, the objective of EW may be to maximize the alignment of estimated weights with golden relatedness values. Indeed, the literature (e.g., [91, 92, 94]–[96]) has established gold–standard–based evaluation protocols that typically compare estimates of relatedness measures with gold annotations using Pearson’s correlation coefficient or Spearman’s rank correlation [98]. Such annotations are typically confined to weights between predefined or generic words for the “intrinsic evaluation” [95] of relatedness measures. In contrast, before AKE, which keyphrases are extracted remains veiled. Even a small textual dataset easily reaches above 1,0001,000 candidates. Should a gold standard comprising (10002)=499,500 10002=499,500 weights then be prepared? Impractical. Hence, ClueNetwork circumvents elusive gold edge weights by applying the presumption of innocence to qualified relatedness measures (Subsubsection I-C3), and then evaluating whether they construct semantic–percolation–friendly SN topologies under their philosophies of relatedness. So, we define the objective of EW in SNC as “maximization of interpretability” (Subsubsection I-A2). I-C2 How Does EW Work? Distributional Hypothesis. Herein, “applying the presumption of innocence to relatedness measures” means that if some measures adhering to the distributional hypothesis [99, 100] ensure minimal veracity, they are evaluated in terms of interpretability rather than veracity. The hypothesis states that semantically close words tend to co–occurr in close contexts [92, 95, 96, 99, 100] and a word’s sense is determined by its neighbors [95, 99, 100]. More relevantly, “close contexts” signify context windows (in this paper, documents), and more modernly, “distributions” signify vector representations of words (in this paper, DTM columns). As some measures based on the hypothesis facilitate weighting word relatedness without considering explicit relations, they are also considered to capture “implicit” word relations [94]. Although termed a “hypothesis,” the hypothesis and its descendants function as de facto axioms in the field of NLP (e.g., [101]–[104]). ClueNetwork also accepts it as such, questioning the selected EW measures: “Do you follow the distributional hypothesis?” (Subsubsection I-C3) Beliefs as Ingredients and Simplified Taxonomy of Semantic Relatedness Measures. Looking across the literature [91]–[97], there are three main sides of semantic relatedness measures (Fig. 7). First, the knowledge–based side estimates relatedness by exploiting some knowledge bases [93, 95], in which explicit word relations are encoded [92]. Next, the distributional side is precisely the side following the distributional hypothesis [91, 92, 95]. Finally, the hybrid side believes estimating relatedness requires considering not only explicit relations but also implicit relations favored by the distributional side [95, 96]. Readers interested in which measures belong to these sides may consult the specialized review papers [92, 93], [95]–[97]. Figure 7: Simplified Taxonomy of Semantic Relatedness Measures. A more relevant point is that, in terms of SNC, a relatedness measure x as “some putative agent” [9] also injects beliefs as ingredients into an SN, such as “Given their relations, the degree of connection between terms a and b is 0.70.7.” That is, x judges the world to be one where the edge weight is 0.70.7 depending on its philosophy of relatedness. For theoretical impartiality, this paper avoids definitive commentary on the general performances of these sides. They can be better or worse depending on downstream tasks. Nonetheless, only several simple distributional measures have been selected for the PoC of ClueNetwork. As discussed in the case of the square circle, target datasets for SNC are largely context–dependent. We have a concern that the other sides consider more generic explicit relations. Given that the distributional side is adaptive to domains, languages, and lexicons [92, 96], it appears suitable for SNC. Selected EW Measures. The selected semantic relatedness measures, hereafter referred to as EW measures, are presented in Table IV. Given that these are well–established simple measures, we believe readers can sufficiently grasp their underlying philosophies by examining the presented formulas and components. Accordingly, only aspects most relevant to the remainder of this paper are briefed here. Co–occurrence Frequency (CF) believes the larger the intersection of individual document sets in which two keyphrases occur, the greater the relatedness. Dice Coefficient (Dice) [105] and Jaccard Index (Jaccard) [106] are similar to CF, yet Dice and Jaccard apply normalization denominators to avoid the scaling effect of individual set sizes. Because Dice and Jaccard share a monotonically increasing relationship, ranks of their resulting adjacency matrix entries are always identical for an SN. This paper refers to CF, Dice, and Jaccard as discrete (frequency–based) measures. Minkowski Distance [98] measures a point–to–point distance between two keyphrases in a vector space derived from a DTM. Among infinite forms of Minkowski, this paper considers only the popular Euclidean Distance (Euclidean). Cosine Similarity (Cosine) [98] believes the larger the dot product between two keyphrase vectors, the greater their relatedness. Here, when an entry in either vector at any dimension is 0, that dimension contributes 0 to the dot product. Document Mover’s Distance (DMD) is a variant of Earth Mover’s Distance (EMD) [107]. EMD is depicted as the minimum total cost of transporting dirt piles from a supply area to a demand area [108]. Likewise, DMD is defined as the minimum total cost of moving the document–level scores of one keyphrase vector to another. Such a cost is derived by identifying the optimal transport plan matrix, in which individual flow amounts are defined. In short, DMD believe the lower the semantic transport cost between two keyphrases, the greater their relatedness. This paper refers to Minkowski, Cosine, and DMD as vector–based measures. TABLE IV: Formulas of Selected Edge Weighting Measures Measure Formula Meanings of Components Co–occurrence Frequency CF(ti,tj)=|(ti)∩(tj)|CF(t_i,t_j)=|O(t_i) (t_j)| • tyt_y: yyth term. • (ty)O(t_y): Set of windows where tyt_y occurs. • |…||…|: Size of a given set. Dice Coefficient [105] Dice(ti,tj)=2|(ti)∩(tj)||(ti)|+|(tj)|Dice(t_i,t_j)= 2|O(t_i) (t_j)||O(t_i)|+|O(t_j)| • As defined in Co–occurrence Frequency. Jaccard Index [106] Jaccard(ti,tj)=|(ti)∩(tj)||(ti)∪(tj)|Jaccard(t_i,t_j)= |O(t_i) (t_j)||O(t_i) (t_j)| • As defined in Co–occurrence Frequency. Minkowski Distance [98] Minkowski(i,j)=[∑k=1m|ti,k−tj,k|p]1/pMinkowski(t_i,t_j)= [ _k=1^m|t_i,k-t_j,k|^p ]^1/p • yt_y: yyth column vector of a given DTM. • m: The number of rows of the DTM. • ty,kt_y,k: kkth entry of yt_y. • |…||…|: Absolute value of a given scalar. • p: When p=1p=1, this measure corresponds to the Manhattan distance (cf. L1L_1 norm), and when p=2p=2, this measure becomes the Euclidean distance (cf. L2L_2 norm). Cosine Similarity [98] Cosine(i,j)=i⋅j‖i‖2‖j‖2Cosine(t_i,t_j)= t_i·t_j\|t_i\|_2\|t_j\|_2 • i⋅jt_i·t_j: Dot product between it_i and jt_j. • ‖…‖2\|…\|_2: L2L_2 norm of a given vector. Document Mover’s Distance [107] • P: Transportation plan matrix. • ≥0P≥ 0: All entries of P are non–negative. • klP_kl: Flow amount from ti,kt_i,k to tj,lt_j,l. • xd_x: xxth row vector of the DTM. • Euclidean(k,l)Euclidean(d_k,d_l): Physical transport distance from ti,kt_i,k to tj,lt_j,l. DMD(i,j)=min≥0∑k,l=1m[kl⋅Euclidean(k,l)],DMD(t_i,t_j)= P≥ 0min _k,l=1^m [P_kl·Euclidean(d_k,d_l) ], subject to ∑l=1mkl=ti,k and ∑k=1mkl=tj,l∀k,lsubject to _l=1^mP_kl=t_i,k and _k=1^mP_kl=t_j,l\;\ ∀\;\ k,l To adhere to the higher–is–closer convention, although Euclidean and DMD are termed “distances,” ClueNetwork normalizes their resulting values by “a suitable inverse function” [93] 1−dist(i,j)/max(dist(x,y))1-dist(t_i,t_j)/max(dist(t_x,t_y)). Herein, dist(i,j)dist(t_i,t_j) is the distance between two keyphrases. Meanwhile, although the range of Cosine is between −1-1 and 11, in ClueNetwork, Cosine yields only non–negative edge weights within a 0 to 11 range, as all DTM entries are non–negative (cf. (1)). Construction of 1–mode Matrix. How, then, do the selected measures specifically work within SNC? When constructing a raw SN, a Term–Term Matrix (∈ℝl×lTTM ^l× l) whose rows and columns are both dimensioned by l keyphrases selected based on (2) for SN sparsification, is built first. Here, the vector–based or discrete measures intervene in distinct manners, respectively. When undertaking such a task with a vector–based measure, DTM columns are first regarded as vector representations of keyphrases. Then, the measure estimates relatedness weights between these vectors. It results in a TTM whose entries are weights of possible edges. When constructing such an adjacency matrix TTM using a discrete measure, a ∈ℝm×lDTM ^m× l is first converted into a binary matrix B whose entries simply indicate whether each keyphrase is present (11) or absent (0) in each document. Then, a raw TTM is built by computing ⊤B B whose entries are CFs between keyphrases. Finally, these entries are updated by applying the measure, thereby resulting in the final TTM. Meanwhile, whether directionality is assigned to edges is also a consideration. When representing an undirected SN, a symmetrical TTM is first built, and then keyphrases are linked with undirected edges derived from either the Strictly Upper Triangular Matrix (SUTM) or the Strictly Lower Triangular Matrix (SLTM). When representing a directed SN, both matrices are used, as they encode distinct directions. Whether undirected or directed, the main diagonal (i.e., loop edges) is typically excluded from SNC. In practice, undirected SNs are more widely used [19] due to a few constraints (Appendix C). This paper also focuses on undirected SNs, and potential extension to directed SNs is left for future work. I-C3 Separate Penguin from Orca Distributional Hypothesis Revisited. Although Minkowski is familiar and DMD appears calculative, we should avoid jumping to the next stage too hastily. Let us suppose that a swimming penguin is positioned at (0,0.5)(0,0.5) on a maritime coordinate plane, and an orca at (0.5,0)(0.5,0) spots the penguin. Given that (0,0)(0,0) is a relative origin in that physical space, we can meaningfully state that their Euclidean distance is approximately 0.710.71 (Fig. 8–a). In contrast, in a DTM (Fig. 8–b), zero signifies that a keyphrase does not occur in a document. Given that there are no documents in which penguin and orca co–occur (i.e., penguin is safe), the edge weighted by Euclidean between penguin and orca is a false positive (Fig. 8–c). Given that ice shelf co–occurs with both penguin and orca once, the edges omitted by Euclidean are false negatives. Figure 8: Behaviors of Euclidean Distance in Different Worlds. Such false edges certainly violate not only intuition but also the distributional hypothesis. What causes such violations? It is the component |ti,k−tj,k|p|t_i,k-t_j,k|^p in Minkowski. It yields a non–zero value even when only one of ti,kt_i,k and tj,kt_j,k has a small non–zero value. DMD incorporating Euclidean [107] is also not free from this problem. That is, Minkowski is vulnerable to noise in spaces (particularly, sparse high–dimensional spaces) where zero is meaningless. This vulnerability has been theoretically [109] and empirically [109, 110] proven. Readers interested in it may consult Appendix D or [109, 110]. Indeed, Euclidean or EMD are more commonly considered in the field of computer vision [12, 13, 107, 108] rather than NLP. Why? In dense 2– or 3–dimensional spaces, zero can be meaningful [109, 110]. There are countless measures in the world. Manually confirming which ones are suitable for SNC can be challenging for peers. Hence, ClueNetwork incorporates the following pretest to question candidate measures: “Do you follow the distributional hypothesis?” Minimal Veracity Pretest. Its basic concept is to filter out liar measures by quantifying anti–false edge abilities of candidate measures. Such an ability is defined as the Matthews Correlation Coefficient [26, 11] of an EW measure: MCC=TP×TN−FP×FN(TP+FP)(TP+FN)(TN+FP)(TN+FN). array[]rMCC= TP×TN-FP×FN (TP+FP)(TP+FN)(TN+FP)(TN+FN). array (3) Herein, for a DTM, “TP (True Positive)” is the number of TTM entries correctly set as non–zero; “TN (True Negative)” is the number of TTM entries correctly set as zero; “FP (False Positive)” is the number of TTM entries falsely set as non–zero; “FN (False Negative)” is the number of TTM entries falsely set as zero. For a textual dataset, when two keyphrases do not co–occur in any document, a veracious measure must set their corresponding TTM entry to zero. When they co–occur in at least one document, the measure must set the entry to a non–zero value. Such passers attain the maximum MCC of 11, whereas failures attain less than 11 and are filtered out. When the denominator of MCC is zero, special criteria are applied: Specifically, when all ground truths (actual co–occurrences) are non–zero (or zero) and predictions perfectly match them, MCC=1MCC=1 is legitimately assigned to a given measure. In contrast, when the measure sets all entries as non–zero (or zero) regardless of actual co–occurrences, MCC=0MCC=0 is assigned, given its lack of discriminative power. Why is the choice of MCC justified? MCC penalizes or rewards all components of the confusion matrix [112]. Thereby, it is suitable for detecting bad measures that link penguin with orca or separate both from ice shelf. Here, the well–established MCC is certainly not our creation. However, the idea of applying it to verify whether EW measures adhere to reality (i.e., the distributional hypothesis) constitutes a touch of novelty. In Subsubsection I-D2, this pretest is performed. I-D Community Detection I-D1 Why Does CD Matter, and What is it? Necessity in SNC. Whether Community Detection (CD) is essential for SNC can be an open question. About 37% of applications are satisfied with raw SNs [19]. However, when an interpreter encounters a raw SN with many vertices and edges in its unpartitioned state, a reaction like “Let me see. Uhhh… how am I supposed to interpret this?” can escape. Here, social scientists often view a community in an SN as something akin to a “topic” [113, 114] in topic modeling that facilitates interpretation [2]. Computer scientists also often believe that a community reveals its members and their interactions distinct from the outside [115]. Accordingly, ClueNetwork leverages CD to alleviate such uhhh moments. Community Detection (CD). For a network (,)G(V,E), where V and E represent the sets of vertices and edges, respectively, a community Ui∈the set of communities U_i set of communities U is a group whose member vertices “satisfy the condition” [115] of having stronger (denser) “intra–group” [117] connections and weaker (sparser) “inter–group” [117] connections [21, 115, 116, 117]. And CD is “to design a mapping” [116] (or “partition” [118]) that regards every vj∈v_j as a member of at least888“At least” indicates that certain works assume overlapping communities. For convenience, the current PoC assumes that Ui∩Uj=∅∀i≠jU_i∩ U_j= \;\ ∀\;\ i≠ j. one community [116]. Maximization of Distinctiveness. That is, satisfying the above condition across all vi∈v_i is equated to the objective of CD. Many criteria, termed Community Scoring Functions (CSFs), for evaluating such objective achievement have been accumulated [119]. In applications like SNC where gold–standard communities are elusive, internal CSFs such as Triad–Participation–Ratio (TPR) [120], Conduction [121], or Modularity Q [21, 24] can be considered [115]. As these CSFs interpret the objective in different ways, [120] first classified such objective achievement into four properties (separability, density, cohesiveness, and clustering coefficient) for gold–standard–based meta–evaluation. Then, [120] demonstrated that while TPR aligned best with density, cohesiveness, and clustering coefficient, and Conduction best with separability, Modularity Q did not. For brevity, these four properties are hereafter collectively referred to as distinctiveness — as the objective ultimately says that communities should be somehow distinct. Accordingly, the objective is also referred to as the maximization of distinctiveness. Meanwhile, Q is used not only as a CSF but also as an objective function that certain CD algorithms aim to maximize. [122] pointed out that when a network is sufficiently large, a partition yielding a higher Q may merge genuinely distinct small communities into a single larger community. Hence, [122] proposed the Constant Potts Model (CPM) as an alternative objective function. Readers interested in specific definitions of TPR, Conduction, the four properties, or CPM may consult the original references. Material Is All We Need. In short, we already know Q is not the most ideal CSF. We nevertheless have employed it in the PoC of ClueNetwork. Why? The PoC is just a PoC. Its true aim is to demonstrate that if a researcher chooses a stage–specific evaluation criterion, SNC pipelines can be ranked within its rule. We have only employed Q as material to achieve this very aim. That is, while considering alternatives is important in future applications, it is outside the current scope. Nonetheless, we considered using the combination of TPR and CPM. Given that some implementations of the selected modularity–based algorithms support Q but not CPM, we have fixed the criterion to Q for a fair comparison. Modularity −1≤Q≤1-1≤ Q≤ 1 [21, 24] can be mathematically defined as the basic form (4)–a or the long form (4)–b: Q=12m∑ij[ij−kikj2m]δ(ci,cj)⋯(a)=∑l[∑ijijδ(ci,l)δ(cj,l)2m−∑ikiδ(ci,l)2m∑jkjδ(cj,l)2m]⋯(b) array[]rQ= 12m _ij [A_ij- k_ik_j2m ]δ(c_i,c_j)·s(a)\\ \\ = _l [ _ijA_ijδ(c_i,l)δ(c_j,l)2m- _ik_iδ(c_i,l)2m _jk_jδ(c_j,l)2m ]·s(b) array (4) For an undirected weighted graph G, the meanings of the components in (4)–b are also presented in Table V. TABLE V: Meanings of Components in (4) Component Meaning l Individual community within G. m Total sum of edge weights in G. A Adjacency matrix of G. δ Kronecker delta function that returns 11 if two communities are identical, and 0 otherwise. kik_i Total weight of edges incident to vertex viv_i. uiu_i Index of the community to which viv_i belongs. Readers encountering this formula likely fall into two groups. Those who are familiar with Q may find nothing new. We kindly encourage them to skip to the next subsubsection. Those who have never encountered Q in their respective fields may experience uhhh moments. But that is fine. The qualitative definition and the belief behind it are all you need. Q is qualitatively defined as the global sum of all local differences between the following components [21, 24]: • the normalized actual sum of intra–community edge weights of a community UlU_l under a candidate partition • the normalized expected sum of intra–community edge weights of UlU_l under a null model. Herein, the null model is a hypothetical model if all edges in G were randomly rewired while retaining the degrees kik_i and kjk_j as well as the community indices uiu_i and uju_j for all vertex indices i and j. That is, the belief behind Q is that a candidate partition is deemed more distinct when its intra–community edges are significantly denser than those of a null model whose edges are connected without any strategy. Why is such a null model necessary? In the absence of a gold–standard partition, a baseline is essential for comparison to justify why one partition is superior to another. I-D2 How Does CD Work? Belief as Ingredients and Simplified Taxonomy of CD Algorithms. According to [117], four main methodological streams have contributed to CD over the last two decades: First, modularity–based algorithms are precisely those that largely formulate CD as a problem to optimize Q or its alternatives (e.g., CPM [122]). Second, spectral clustering methods perform CD by exploiting spectral properties (i.e., eigenvalues and eigenvectors) of the graph Laplacian matrix derived from a given adjacency matrix. Figure 9: Simplified Taxonomy of Community Detection Algorithms. Third, probabilistic models fundamentally regard a network as an uncertain system. They also assume that if certain vertices belong to the same community, such vertices are more likely to be connected. Hence, they aim to uncover the underlying structure (i.e., community structure) of such uncertainty by estimating latent variables and parameters from observed variables and their probability distributions. Fourth, deep learning approaches leverage the capability of deep neural networks to learn patterns in complex data structures (e.g., networks) and to represent their basic elements (e.g., vertices), dependencies (e.g., edges), and larger elements (e.g., subgraphs) as informative features. Communities are then identified by exploiting such features. In terms of SNC, a CD algorithm x as “some putative agent” [9] also injects beliefs as ingredients into an SN, such as “a keyphrase viv_i belongs to a topic UlU_l.” That is, x judges the world to be one where viv_i belongs to UlU_l. Based on their respective philosophies of distinctiveness, CD algorithms hold such beliefs by focusing on Q, spectral properties, probabilistic patterns, or representational features. Readers interested in which algorithms belong to these streams may consult the comprehensive review paper [117]. Furthermore, [115] and [116] are excellent review papers that are specialized in deep learning–based or probabilistic CD algorithms. Selected CD Algorithms. The experiment in [117] suggests that no stream is clearly superior to the others. Peers may choose the streams with which they are most familiar. We have employed highly accessible modularity–based algorithms as shortcuts to the PoC. As these are well–established, only their high–level summaries are provided here. We clarify that their beliefs regarding SN distinctiveness do not differ, as their shared objective function is its very interpretation. They differ only in how they optimize such a function. The Clauset–Newman–Moore algorithm (CNM) [24] is an early greedy algorithm. It selects a vertex merger (Fig. 10–a) that yields the best possible Q change at each iteration, without considering long–term alternatives. Such merging is iterated until all original vertices are merged into the same community, after which the partition that yields the best Q among all recorded partitions is selected as the final partition. Figure 10: Examples of Higher–level Vertices, Singleton Communities, Badly Connected Community, Parent Community, and Subcommunities. CNM’s limitation is that original vertices are irreversibly merged because CNM directly regards higher–level vertices as communities (Fig. 10–a). Hence, at the initial step, the Louvain algorithm (Louvain) [25] regards each vertex as the sole member of a singleton community (Fig. 10–b) rather than the community itself. Vertices can then be moved to other communities multiple times until no further improvement in Q is possible. Only after such a phase does Louvain regard temporary communities as higher–level vertices (Fig. 10–a) to iterate the phase (Fig. 10–b), yielding the final partition. The Leiden algorithm [118] cautions that Louvain’s focus on vertex moves can generate badly connected communities whose certain members can only reach each other through paths extending outside their community (Fig. 10–c). After early vertex moves, Leiden refines a given temporary partition by allowing members of every parent community to form subcommunities (Fig. 10-d). Retaining the temporary partition, Leiden then regards subcommunities as higher–level vertices. Here, they can move to other parent communities. Such moving and refining are iterated until no further improvement in Q is possible, yielding the final partition. Leiden also uses a strategy during such refinement similar to the exploitation versus exploration method in reinforcement learning [123]. That is, while moves yielding maximal improvements in Q are preferentially exploited, those yielding mere improvements can also be randomly selected. Such randomness (pa. β) leaves room for uncovering optimal partitions that CNM or Louvain would otherwise miss. Finally, although the Fast Label Propagation Algorithm (FLPA) [124] is categorized as a modularity–based algorithm [117], it does not explicitly optimize any objective function. Instead, the quality of its outputs can be evaluated in terms of Q. FLPA operates on a highly intuitive mechanism. It iteratively reassigns community labels until the label of each vertex becomes the one most shared among its neighbors. I Local Evaluation Section I has covered one fold of the subject matter through a review of SNs as clues and the three SNC stages. This section first defines and justifies the local evaluation criteria for ranking SNs (Subsection I-A), and then presents illustrative experiments based on the criteria (Subsubsections I-C1–I-E1). Hence, it is a significant part of the other fold for the PoC of ClueNetwork. Here, while Subsection I-B describes the general experimental setup, Subsubsections I-C1–I-E1 describe the stage–tailored setups. I-A Local Evaluation Criteria Firstly, this subsection addresses RQ5 (“How are the local evaluation criteria defined and justified?”). Here, hF1hF_1 and RI are defined and justified in Subsubsections I-A1 and I-A2, respectively. Given that we have already defined and justified Modularity Q in Subsubsection I-D1, readers may consult that section for details on Q. I-A1 Harmonic F1 Score Definition. For the PoC, the selected AKE algorithms are evaluated by using the harmonic F1F1 score hF1hF_1. The definitions999We have referred to the natural–language–based description adopted by [49], which is more intuitive than the confusion–matrix–based description. of hF1hF_1 and relevant criteria are presented in Table VI. Herein, the “total number of gold keyphrases” is the number of keyphrases assigned as gold standards to a document. This number, denoted as a variable υ , is the number of prioritization opportunities allowed for an AKE algorithm x on that document [127]. That is, the task of x is to maximize, within υ , matches between prioritized candidates and the gold keyphrases by ranking candidates; the essence of the evaluation is to assess such prioritizing capabilities of algorithms. TABLE VI: Possible Evaluation Criteria in AKE Name (Symbol) Definition Exact Precision (P) =Number of Exactly Matched CandidatesTotal Number of Prioritized Candidates= Number of Exactly Matched CandidatesTotal Number of Prioritized Candidates Exact Recall (R) =Number of Exactly Matched CandidatesTotal Number of Gold Keyphrases= Number of Exactly Matched CandidatesTotal Number of Gold Keyphrases Exact F1 (F1F_1) =2(P×R)P+R= 2(P×R)P+R (Harmonic Mean of P and R) Partial Precision (pPpP) =Number of Partially Matched CandidatesTotal Number of Prioritized Candidates= Number of Partially Matched CandidatesTotal Number of Prioritized Candidates Partial Recall (pRpR) =Number of Partially Matched CandidatesTotal Number of Gold Keyphrases= Number of Partially Matched CandidatesTotal Number of Gold Keyphrases Partial F1 (pF1pF_1) =2(pP×pR)pP+pR= 2(pP× pR)pP+pR (Harmonic Mean of pPpP and pRpR) Harmonic F1 (hF1hF_1) =2(F1×pF1)F1+pF1= 2(F_1× pF_1)F_1+pF_1 (Harmonic Mean of F1F_1 and pF1pF_1) Interestingly, using υ instead of a constant makes precision and recall equivalent, as their denominators become identical. If a constant is used instead, while precision rewards algorithms that maximize matches within that constant, recall rewards algorithms that retrieve as many gold keyphrases as possible, regardless of the constant. In either case, F1F_1 [125] is the standard criterion in the field (e.g., [49, 51, 58, 59, 62, 63, 71, 79, 81, 82, 85], and [86]). Justification of Selection. Nonetheless, pF1pF_1 serves as a compelling alternative in the field (e.g., [49], [51], and [81]), given that F1F_1 imposes strict penalties on prioritized candidates (i.e., extracted keyphrases) unless they exactly match gold keyphrases, regardless of semantic relatedness [51]. In contrast, in partial matching, if gold keyphrases are (happy, cat), (meme) and extracted ones are (huh, cat), (meme), these sets are decomposed into (happy), (cat), (meme) and (huh), (cat), (meme), respectively. F1F_1 calculated based on such newly formed sets is pF1pF_1. It sometimes prioritizes trivial unigrams that lack sufficient contextual relevance [51]. That is, there is a trade–off between F1F_1 and pF1pF_1. In general, a harmonic mean is accepted as a canonical mathematical mechanism (e.g., F1F_1) that strictly penalizes the final value if either of two trading–off components is excessively low. Then, is there any reason not to adopt hF1hF_1 as a form of nested harmonic mean? If the field can accept pF1pF_1, it can also accept the stricter hF1hF_1, given that hF1hF_1 does not measure an entirely different dimension. We clarify that this paper does not argue that hF1hF_1 must be used exclusively for SNC. I-A2 Robustness Improvement (RI) For the PoC, the selected EW measures are evaluated by using RI. Unlike hF1hF_1, deduced from F1F_1 and pF1pF_1, RI has been derived by introducing a touch of novelty to the well–established percolation theory, a necessity born out of scenarios where gold–standard-based evaluation remains elusive (Subsubsection I-C1). Hence, more thorough background, motivation, and justification are presented below. Facets of Distribution. Let us begin with a fact based on the distributional hypothesis. If an EW measure passes the minimal veracity101010The term “veracity” occurs repeatedly throughout this paper. We clarify that our notion of it refers to the property of aligning with ground–truth. pretest, within the system where the given DTM is assumed to be true, it does not generate false edges, and its belief that the relatedness between terms a and b is 0.70.7 reflects a certain facet of the DTM. That is, if CF or Cosine holds that belief, although neither determines the 0.70.7 by encapsulating all possible facets of the DTM, the 0.70.7 is an inevitable consequence derived from the DTM, not others. Hence, the beliefs of CF and Cosine are distinct, not correct or incorrect, and a possible error between the 0.70.7 and a possibly existing but elusive gold weight is no longer an issue. From Veracity To Interpretability. Against this backdrop, we enter an alternative detour to facilitate ranking EW measures. Let us suppose that nine “extracted keyphrases,” hereafter referred to as “keyphrases” for brevity, form two SNs (Fig. 11), each consisting of three edges. Although it is elusive which SN is more veracious, Fig. 11–b appears more suitable for exploratory research (Subsection I-A). Figure 11: Which SN Maximizes Interpretability? Why? Its hubs (mediators) v2v_2 and v5v_5 manifest the latent edges among v2,v6v_2,v_6, and v7v_7. The presence of such hubs prompts an interpreter to generate hypotheses that mediated vertices also somehow percolate their semantics through each other. In contrast, Fig. 11-a forms the closed triangle, decreasing potential wow moments of abduction. Hence, we define the interpretability of an SN as follows and regard the objective of EW as the maximization of interpretability: • the property of prompting an interpreter’s hypothesis generation whereby hubs are deployed. Fair Rule is All We Need. Here, a consideration arises. As explained above, CF and Cosine operate under different beliefs, making it natural that hub deployments they yield differ. Therefore, directly comparing hub deployments of resulting SNs from CF and Cosine is unfair. In physics, however, there is an established fair criterion: Output−BaselineMaximum Possible−Baseline Output-BaselineMaximum Possible-Baseline [128]. TABLE VII: Comparison of Fair Rule Settings (Ours: Top, [128]: Bottom) for Targets with Varying Baselines. f(…)f^(…), ω, and K are defined later. Baseline Treatment Output fnullf^null@(ω, K) EW Measure fempiricalf^empirical@(ω, K) Students’ Average Pre–Test Score Instructional Method Students’ Average Post–Test Score This normalization–based criterion quantifies effects of different treatments applied to different baselines; [128] used it to compare effects of different instructional methods across different physics courses. The basic concept and formula of RI are isomorphic to it (Table VII). Then, the remaining question is as follows: how such an output (i.e., pre–normalization interpretability) and its baseline are defined in terms of EW. Output. Let us first define such an output. According to percolation theory [129], as more vertices act as hubs, they collectively form the largest connected subgraph, termed a giant component (,)G_GC(V_GC,E_GC) [130]. Then, by constructing an SN as a G_GC via an EW measure and removing its vertices one–by–one at random, can we identify its critical threshold fcf_c at which G_GC fragments? Yes, as it is the very approach established by physicists [131]–[133]. Herein, fcf_c is defined as the fraction of removed vertices (|(f)|/|(0)|)/(|(0)|/|(0)|)→0(|V_GC(f)|/|V(0)|)/(|V_GC(0)|/|V(0)|)→ 0, where |(0)|/|(0)||V_GC(0)|/|V(0)| and |(f)|/|(0)||V_GC(f)|/|V(0)| denote each probability that a randomly chosen vertex belongs to G_GC before and after removing a fraction f of vertices from G, respectively [132, 133]. For finite networks of ||<∞|V|<∞, such fragmentation can be regarded as the moment when the size of the second largest connected component111111Why the second largest? Analogous to chopping a tree, the moment it splits in half is far more critical than when minor woodchips fly off. reaches its maximum size during such an empirical simulation [134]. In short, a higher fcempiricalf_c^empirical of an SN (G) signifies that more hubs are deployed in it, thereby exhibiting greater robustness against random vertex failure simulation. Hence, we define the output as fcempiricalf_c^empirical. For reference, fcf_c can also be derived through analytical approximation methods. We clarify that fcf_c in this paper is confined to fcempiricalf_c^empirical, given challenges in applying such methods to empirical networks (Appendix E). Key Properties. Unlike students’ average pre–test score, a baseline fcnullf_c^null against fcempiricalf_c^empirical of G is not pre–given. Hence, fcnullf_c^null of a null model nullG_null generated from G is necessary as an artificial baseline (cf. [21] and [24]). When generating nullG_null, preserving all properties of G makes comparison meaningless. nullG_null should reflect properties to be preserved as preserved, and properties to be varied as varied [141]. The former can be ω and K, while the latter L and T△T_ . First, ω is a specified number of edges to be represented. Together with l (a specified number of vertices to be represented), it constitutes the desired resolution parameters for SN sparsification. As allowing 100100 edges for one EW measure while restricting another to 5050 edges is unfair, ω must be fixed. Second, K is a vertex degree sequence121212For instance, if =v1,v2,v3V=\v_1,v_2,v_3\ and the degrees of v1,v2, and v3v_1,v_2, and v_3 are 1,1 and 21,1 and 2, respectively, then =1,1,2K=\1,1,2\., where the degree of a vertex is the number of edges it has to other vertices [10]. K must be fixed for each SN to ensure valid comparison between fcempiricalf_c^empirical and fcnullf_c^null. Why? If an EW measure determines K of G one way, generating ~null G_null with another ~ K would be akin to comparing against f~cnull f_c^null grounded in another ~ G. Third, the average shortest path length L [10] is defined as L=1||(||−1)∑vi≠vjd(vi,vj), L= 1|V|(|V|-1) _v_i≠ v_jd(v_i,v_j), (5) where d(vi,vj)d(v_i,v_j) is the smallest number of edges to be traversed from viv_i to vjv_j. For an SN, L certainly signifies the average semantic percolation cost between keyphrases (e.g., abcd versus abd). That is, L is an SN interpreter’s visual scanning effort. Therefore, to evaluate the effect of an EW measure, L(null)L(G_null) should be greater than or at least equal to L()L(G). Fourth, transitivity T△T_ [142] is defined as (6), and, for an SN, T△(null)T_ (G_null) should also be greater than or at least equal to T△()T_ (G). Why? A high proportion of triangles can delay an SN interpreter’s visual scanning due to their circular connectivity. Indeed, [139] suggests that a higher T△T_ can hinder smooth interactions (i.e., percolation) among vertices. T△=6N△2N3, T_ = 6N_ 2N_3, (6) where N3N_3 and N△N_ are the numbers of connected triples (e.g., not only △ but also a–b–c) and triangles (closed triples), respectively; each triangle manifests in six different permutations depending on a starting vertex and a direction (e.g., abca, bcab, cabc, …..., and cbac) of semantic cycling (thus, N△N_ is multiplied by 66); for a connected triple, only two directions (e.g., abc and cba) through which semantics percolate need to be considered (thus, N3N_3 is multiplied by 22). Baseline. To adhere to these requirements for ω, K, L, and T△T_ , we have slightly modified the established ClustRNet algorithm (null model generator) [141]. ClustRNet generates nullG_null by introducing randomness while adhering to the requirements for ω, K, and T△T_ , but it does not account for L. Our modified version (Algorithm 1) accounts for L. As ClustRNet also employs a configuration model [135] as the initial candidate null model (0)′G _(0), ClustRNet is prone to enter an infinite loop if any candidate null model ′G fails to remain connected. Algorithm 1 avoids such a loop by setting (0)′G _(0) as a copy of a connected G. Edge rewiring is then performed to monotonically increase both T△(′)T_ (G ) and L(′)L(G ). Adhering to K, Algorithm 1 terminates when T△(′)T_ (G ) and L(′)L(G ) approach (1+z)T△()(1+z)T_ (G) and (1+z)L()(1+z)L(G), respectively, or when a maximum h iterations are reached. How, then, is such a connected G obtained? First, for a given ∈ℝl×lTTM ^l× l, established Kruskal’s algorithm [143] extracts a Maximum Spanning Tree (MST) that serves as the backbone of G by prioritizing higher–weighted TTM entries. Next, additional higher–weighted TTM entries are sequentially added to the MST until the total number of edges reaches ω, thereby constructing G. Ultimately, the critical threshold of nullG_null generated for G is the very baseline fcnullf_c^null. Definition. Therefore, 0≤RI≤10 ≤ 1 is mathematically defined as (7), where G’s fcempiricalf_c^empirical and nullG_null’s fcnullf_c^null are obtained through respective vertex random failure simulations: RI=fcempirical−fcnull1−fcnull, if fcempirical>fcnull;0, otherwise. = (7) (7) can also be qualitatively regarded as the proportion of additional SN interpretability gained relative to the total possible SN interpretability improvement. A higher RI signifies a greater effect of an EW measure on hub deployment activating multiple alternative routes for semantic percolation. Here, the well–established Output−BaselineMaximum Possible−Baseline Output-BaselineMaximum Possible-Baseline [128], percolation theory [129], ω, K [10], L [10], T△T_ [142], and ClustRNet [141] are not our creations. Nonetheless, the idea of integrating them to facilitate ranking raw SNs (ultimately, their EW measures) humbly constitutes a touch of novelty. Justification. Here, one can legitimately demand, “Validate whether RI actually harmonizes with the common sense of interpretability improvement.” Reasonable, and we will do so. To this end, we first operationally define the “Interpretability imProvement (IP)” as two aspects: TABLE VIII: Overview of Benchmark Datasets Document Type Dataset Annotator Type #Case Avg #Tokens Max #Tokens Avg #Goldens Scientific (full–text papers) SemEval–2010 [144] Authors and Students 244244 8821.978821.97 1734717347 15.0015.00 NUS [145] Authors and Students 211211 9773.899773.89 1837518375 11.0711.07 Scientific (paper abstracts) Inspec [146] Professional Indexers 20002000 159.75159.75 672672 9.659.65 KDD [147] Authors 754754 216.79216.79 446446 4.074.07 W [147] Authors 13301330 185.62185.62 664664 4.804.80 Scientific (paper paragraphs) SemEval–2017 [148] An Expert and Students 500500 237.55237.55 499499 17.2917.29 Common (news articles) DUC–2001 [63] Students 308308 964.20964.20 63756375 8.068.06 500N–KP–Crowd [149] Crowdsourced Annotators 500500 591.27591.27 79477947 48.9348.93 IP=IP1=L(null)−L()L(null)(L(null)≥L())IP2=T△(null)−T△()T△(null)(T△(null)≥T△()) = (8) Based on the established L and T△T_ , (8) quantifies the relative reduction (achieved by using an EW measure) in an SN interpreter’s visual scanning effort for identifying relatedness between two keyphrases. Ultimately, hypothesis generation is subject to the interpreter’s expertise. Nonetheless, it is an objective fact that larger IP1IP_1 and IP2IP_2 at least foster a more interpretable condition. Hence, in Subsubsection I-D2, we validate correlations between RI and these two aspects. Input: Connected (,,)G(V,E,K), h, and z Output: Connected null(,null,)G_null(V,E_null,K) ⊳ Main Steps Generate the initial (0)′G _(0) by copying G for i in [1,h][1,\;\ h] do (i)′←(i−1)′G _(i) _(i-1) Select vav_a (ka>1k_a>1) ∈(i)′ _(i) uniformly at random Select two neighbors, vbv_b and vcv_c, of vav_a uniformly at random such that kb>1k_b>1, kc>1k_c>1, and vb≠vcv_b≠ v_c Select a neighbor, vdv_d of vbv_b, and a neighbor, vev_e of vcv_c, uniformly at random such that vd≠vav_d≠ v_a, ve≠vav_e≠ v_a, and vd≠vev_d≠ v_e if (vb,vc)(v_b,v_c) and (vd,ve)(v_d,v_e) ∉(i)′ _(i) then Remove (vb,vd)(v_b,v_d) and (vc,ve)(v_c,v_e) from (i)′E _(i) Add (vb,vc)(v_b,v_c) and (vd,ve)(v_d,v_e) to (i)′E _(i) VALID:=FALSEVALID:=FALSE if T△((i)′)>T△((i−1)′)T_ (G _(i))>T_ (G _(i-1)), L((i)′)>L((i−1)′)L(G _(i))>L(G _(i-1)), T△((i)′)≤(1+z)T△()T_ (G _(i))≤(1+z)T_ (G), L((i)′)≤(1+z)L()L(G _(i))≤(1+z)L(G), and (i)′G _(i) is connected then VALID:=TRUEVALID:=TRUE if T△((i)′)≥0.95(1+z)T△()T_ (G _(i))≥ 0.95(1+z)T_ (G) and L((i)′)≥0.95(1+z)L()L(G _(i))≥ 0.95(1+z)L(G) then null:=(i)′G_null:=G _(i) return nullG_null end if VALID is FALSE then Add (vb,vd)(v_b,v_d) and (vc,ve)(v_c,v_e) to (i)′E _(i) Remove (vb,vc)(v_b,v_c) and (vd,ve)(v_d,v_e) from (i)′E _(i) end end end return nullG_null Algorithm 1 Null Model Generator I-B General Experimental Setup We now explain the general experimental setup prepared to answer RQ6 (“Which stage–specific selected methods yield high performance?”). Later, Subsubsections I-C2–I-E2 themselves serve as the very answers. Datasets. Eight benchmark datasets (Table VIII), widely employed in the field of AKE (e.g., [49, 51], [58, 59], [61]–[63], [71, 79, 81, 82, 85], and [86]), were used in the illustrative experiments. Every incomplete case (missing ID, document, or gold keyphrases) had been excluded from all datasets. As one (link 1) of the dataset distributors (link 1)(link 2) provided some datasets in tokenized forms, we restored them to original or near–original forms. Regarding the latter, the algorithms remain under fair conditions and should be adaptive. Given that BERT variants typically have an input limit of 512 tokens [88], KeyBERT and MDERank were only evaluated on KDD and SemEval–2017. Although MPNet has a shorter limit of 384 tokens [90], average pooling allows LMRank to overcome that constraint [81]. General Process of local evaluation in ClueNetwork is as follows. In Stage 1 (Subsection I-C), average hF1hF_1 scores of AKE algorithms on each dataset are evaluated. In Stage 2 (Subsection I-D), top–l keyphrases of each AKE algorithm are first identified, and then corresponding TTMs ∈ℝl×l ^l× l are built by using EW measures. Based on ω, raw SNs are extracted from those TTMs, and then their RI scores are evaluated. In Stage 3 (Subsection I-E), CD algorithms are applied to the SNs and corresponding Q scores are evaluated. For Reproducibility. All relevant code, random seeds, parameters, preprocessing, intermediate or final outputs, and the versions of employed Python packages have been disclosed at here (link). As our laptops are digital fossils, all relevant experiments have been conducted in a cloud environment: • Cloud Environment: Google Colab (Pro) • System Type: x86_64 with 6464–bit architecture • CPU: Intel(R) Xeon(R) CPU @ 2.20 GHz (Family 6, Model 85, Stepping 7), 66 cores with 1212 threads • GPU: NVIDIA L4 (22.522.5 GB VRAM, Driver v550.54.15) • RAM: 5454 GB (Details are not provided by Google) • Storage: 250250 GB NVMe SSD • OS: Ubuntu 22.04.4 LTS (Kernel 6.6.105+) • Programming Language: Python 3.12.12 TABLE IX: Experimental Settings for AKE Algorithms (algos.) Algo. (Existing Implementation) Target Dataset Employed Parameters Preprocessing TF (We implemented) All the datasets n=3n=3 Type 11 TF–IDF (Link) n=3n=3 KP–Miner (Link) n=5n=5, lasflasf == 33, cutoffcutoff == 400400, σ=3.0σ=3.0, α=2.3α=2.3, and Pf=1P_f=1 YAKE! (Link) n=3n=3, (window)=2(window)=2, and use_stems=Trueuse\_stems=True TextRank (TR) (Link) (window)=2(window)=2, T=33%T=33\%, and δ=0.85δ=0.85 Type 22 SingleRank (SR) (Link) (window)=10(window)=10 and δ=0.85δ=0.85 PositionRank (PR) (Link) (window)=10(window)=10 and δ=0.85δ=0.85 KeyBERT (Link) KDD, SemEval–2017 (language model) == ”all–distilroberta–v1” Type 33 MDERank (Link) KDD, SemEval–2017 (language model) == ”bert–base–uncased” Type 44 LMRank (Link) All except Inspec and 500N–KPC (language model) == ”all–mpnet–base–v2”, deduplicatededuplicate == FalseFalse, keeps_noun_adjskeeps\_noun\_adjs == TrueTrue, positional_featurepositional\_feature == TrueTrue, and μ=1.0μ=1.0 Type 55 Inspec, 500N–KPC (language model) == ”all–mpnet–base–v2”, deduplicatededuplicate == FalseFalse, keeps_noun_adjskeeps\_noun\_adjs == TrueTrue, positional_featurepositional\_feature == FalseFalse, and μ=1.0μ=1.0 I-C Experiment 1: Automatic Keyphrase Extraction We now report the AKE–tailored experimental setup (Subsubsection I-C1) and which of the selected AKE algorithms maximized SN keyness (Subsubsection I-C2). I-C1 Experimental Setup for AKE Implementations. We implemented TF through PositionRank (Table IX) based on the implementations of the Python Keyphrase Extraction toolkit (PKE) [150]. Given that the N–based algorithms are not yet supported by PKE, we tailored their existing implementations for our work. Parameters. Most AKE algorithms incorporate one or more user–specifiable parameters, namely hyperparameters. To focus on the PoC of ClueNetwork, we employed the default parameters whenever appropriate (Table IX). These defaults are also grounded in empirical evidence from the original papers or their subsequent implementations. Readers may opt for alternatives for future applications. Preprocessing, the algorithm itself, and its data adaptability are crucial factors jointly determining the performance of an AKE algorithm. Most AKE algorithms employ their own preprocessing strategies to extract keyphrases exclusively from given phrases. One can specify an n–gram parameter (Table IX) to exclude (n+1)(n+1)–grams and higher, while another can consider only Noun Phrases (NPs) as candidates. As preprocessing manifests in such diverse types, to paradoxically avoid verbosity, we summarize the types employed by the selected algorithms and their details in Table IX and Appendix F, respectively. In short, we have adhered to the strategies of the original papers or implementations. To emphasize preprocessing, we intervened exceptionally in KeyBERT, and details are discussed in Subsubsection I-C2. I-C2 Results of AKE Statistical Analysis. While most AKE algorithms achieve moderate (F1F_1, pF1pF_1, or hF1hF_1) scores for many documents and rarely reach near–perfect scores, they also record zero scores for many other documents. Their score distributions often follow zero–inflated distributions. Indeed, across the selected algorithms and datasets, Table X shows the low (average) hF1hF_1 scores and high variances. For brevity, 95%95\% Bootstrap Confidence Intervals (BCIs) [154] for these averages are separately disclosed at our GitHub (link), where 10410^4 resamples were drawn with replacement from each distribution. Consequently, both the Q–Q plots and the Kolmogorov–Smirnov (K–S) test [155] — whose null hypothesis that a given distribution follows the normal distribution is rejected when p<0.05p<0.05 — indicated that the normality was violated for 6161 of the 6868 hF1hF_1 distributions. An example is presented in Fig. 12. The remaining 6767 pairs of Q–Q plots and K–S test p–values are also disclosed separately (link). TABLE X: hF1hF_1–based Evaluation Results (6868 Pairs of Averages and Standard Deviations) Benchmark hF1@υhF_1@ Statistics–based Algorithms Graph–based Algorithms N–based Algorithms TF TF–IDF KP–Miner YAKE! TR SR PR KeyBERT MDERank LMRank SemEval–2010 Avg 0.1340.134 0.2070.207 0.2870.287 0.1900.190 0.0350.035 0.0530.053 0.1120.112 - - 0.1640.164 Std 0.1090.109 0.1150.115 0.1190.119 0.1190.119 0.0590.059 0.0730.073 0.0920.092 - - 0.0990.099 NUS Avg 0.1440.144 0.2580.258 0.3410.341 0.2330.233 0.0210.021 0.0390.039 0.1130.113 - - 0.1450.145 Std 0.1440.144 0.1670.167 0.1710.171 0.1500.150 0.0540.054 0.0740.074 0.1180.118 - - 0.1360.136 Inspec Avg 0.1250.125 0.2340.234 0.0920.092 0.2600.260 0.1490.149 0.2870.287 0.2870.287 - - 0.3640.364 Std 0.1330.133 0.1630.163 0.1330.133 0.1620.162 0.1570.157 0.1880.188 0.1800.180 - - 0.2000.200 KDD Avg 0.0920.092 0.1750.175 0.1740.174 0.1190.119 0.0840.084 0.0890.089 0.1480.148 0.1460.146 0.1380.138 0.1640.164 Std 0.1590.159 0.2000.200 0.2110.211 0.1790.179 0.1550.155 0.1540.154 0.1870.187 0.1910.191 0.1890.189 0.1990.199 W Avg 0.1230.123 0.1860.186 0.1750.175 0.1180.118 0.0840.084 0.0740.074 0.1220.122 - - 0.1420.142 Std 0.1650.165 0.1920.192 0.2000.200 0.1600.160 0.1530.153 0.1490.149 0.1820.182 - - 0.1820.182 SemEval–2017 Avg 0.2170.217 0.2750.275 0.1400.140 0.2840.284 0.2160.216 0.4260.426 0.3990.399 0.4850.485 0.4630.463 0.2900.290 Std 0.1110.111 0.1190.119 0.1110.111 0.1270.127 0.1250.125 0.1550.155 0.1490.149 0.1540.154 0.1480.148 0.1530.153 DUC–2001 Avg 0.1060.106 0.1600.160 0.1800.180 0.1780.178 0.1240.124 0.2470.247 0.2810.281 - - 0.2400.240 Std 0.1250.125 0.1490.149 0.1540.154 0.1430.143 0.1340.134 0.1670.167 0.1840.184 - - 0.1610.161 500N–KPC Avg 0.3630.363 0.3370.337 0.1930.193 0.3090.309 0.1940.194 0.2970.297 0.3150.315 - - 0.1660.166 Std 0.1070.107 0.0950.095 0.1030.103 0.1060.106 0.0820.082 0.1530.153 0.1380.138 - - 0.0880.088 Figure 12: Q-Q Plot of YAKE! on Inspec. Given such substantial non–normality, the original averages are not reliable representative statistics. It is safer to use new averages derived from rank–transformed distributions and to conduct a non–parametric statistical analysis that relies on such transformation. Hence, to determine whether significant differences exist among the averages (Table X), we performed the Friedman test [156] followed by the Nemenyi post–hoc test [157] at the dataset level. For our matched–samples design, where a document, an AKE algorithm, and a resulting hF1hF_1 score distribution served as a block, a treatment, and a sample (i.e., set of observations), respectively, this non–parametric approach was suitable. For all datasets, Friedman indicated significant differences in the average hF1hF_1 ranks among at least one pair of the AKE algorithms. That is, the null hypothesis (“No such difference exists”) was rejected, as all p–values were less than 0.050.05. Nemenyi then identified which pairs exhibited significance at the dataset level. Its null hypothesis (“No such difference exists”) is also rejected when p<0.05p<0.05. The p–values are disclosed separately (link), while the results are summarized in the Critical Difference (CD) diagrams [158]. The numbers in parentheses denote the average hF1hF_1 ranks. No significant difference exists between any two algorithms directly tied by a string (Fig. 13). Qualitative Analysis. Based on the significant differences (p<0.05p<0.05) presented in Fig. 13 and the statistics in Table VIII, we provide the following post–hoc interpretation: First, TF achieved mid–to–low average hF1hF_1 ranks across most datasets. An exception was 500N–KP–Crowd, characterized by an exceptionally high number of gold keyphrases per document (48.948.9 per document). Meanwhile, KP–Miner exhibited low performance on 500N–KP–Crowd, as its strict cutoff and least allowable seen frequency constrained full exploitation of these abundant prioritization opportunities. Second, these trends were reversed for the full–text paper datasets (SemEval–2010 and NUS) and the abstract datasets (KDD and W). As the former tend to present contributions and novelties early, KP–Miner benefited from its cutoff. Given the lack of prioritization opportunities (4.84.8 per document) for the latter, algorithms must prioritize candidates based on salient features. In this regard, the heuristics of KP–Miner and its baseline (TF–IDF) were effective. Third, the graph–based algorithms achieved mid–to–low average hF1hF_1 ranks for SemEval–2010, NUS, KDD, and W. As words that contribute to topics but do not serve as components of gold keyphrases occur frequently in full–text papers [51], they hinder graph–based algorithms that focus on word associations. Given the limited prioritization opportunities for KDD and W (44 to 4.84.8 per document), word associations appeared less effective than salient features. Figure 13: Critical Difference Diagrams of AKE Algorithms across Datasets. Each value in parentheses is an average of hF1hF_1 ranks across documents. Fourth, nonetheless, PositionRank and SingleRank outperformed the statistics–based algorithms on Inspec, SemEval–2017, and DUC–2001, which feature at least twice as many prioritization opportunities (88 to 17.317.3 per document). As word associations become noteworthy with increasing prioritization opportunities, these algorithms benefited accordingly. Notably, PositionRank achieved its highest performance on the news article dataset (DUC–2001), which typically presents topics in opening sentences. Fifth, when sufficient prioritization opportunities were available (17.317.3 per document), KeyBERT and MDERank achieved the highest performance on SemEval–2017. While KeyBERT, which regards n–grams as candidates by default, had achieved low performance in [81] due to overlapping n–grams reducing diversity of extracted keyphrases, even KeyBERT paired with the less performant (link) all–distilroberta–v1 outperformed LMRank paired with all–mpnet–base–v2 by regarding NPs as candidates (Table IX with Appendix F). This underscores the significance of preprocessing. Sixth, while KeyBERT and MDERank faced the input limit of 512512 tokens, average pooling did not lead LMRank to a definitive breakthrough. Although we expected LMRank to deliver superior performance on the full–text paper datasets, it instead peaked on the abstract dataset (Inspec), where prioritization opportunities per document are 9.79.7. When such opportunities exceeded or fell below that level, LMRank struggled with prioritization (e.g., SemEval–2017 and W). I-D Experiment 2: Edge Weighting We now report the EW–tailored experimental setup (Subsubsection I-D1) and which of the selected EW measures maximized SN interpretability (Subsubsection I-D2). I-D1 Experimental Setup for EW Implementations. DMD was implemented based on [159], while the remaining measures were implemented by us. Parameters. Given that complex SNs overload human cognitive capacity, setting resolution parameters is essential. Accordingly, l and ω were set to the author–fit levels of 5050 vertices and 100100 edges, respectively. For the null model generator (Algorithm 1), h and z were set to 10410^4 and 1.01.0, respectively, to secure the discriminative power of null models. Vertex Random Failure Simulations. We evaluated each row SN based on its average RI obtained from 10310^3 simulation runs, where the random seed is fixed to 20262026. A single run may yield unreliable fcempiricalf_c^empirical and fcnullf_c^null due to the risk of premature hub removals. In contrast, 10310^3 substantially exceeds the empirical threshold of 3030 required for the Central Limit Theorem to hold while avoiding computational overhead. I-D2 Results of EW Veracity Pretest. As explained in Subsubsection I-C3, we conducted the minimal veracity pretest on the EW measures. CF, Dice, Jaccard, and Cosine passed the test, as they recorded MCC=1MCC=1 for all DTMs across every dataset (Table XI). TABLE XI: Veracity Pretest Results of EW Measures (P: PASS, F: FAIL) Data CF Dice Jaccard Euclidean Cosine DMD Sem10 P P P F: 0/80/8 P F: 0/80/8 NUS P P P F: 0/80/8 P F: 1/81/8 Inspec P P P F: 0/80/8 P F: 0/80/8 KDD P P P F: 0/100/10 P F: 0/100/10 W P P P F: 0/80/8 P F: 0/80/8 Sem17 P P P F: 0/100/10 P F: 0/100/10 DUC P P P F: 0/80/8 P F: 0/80/8 500N P P P F: 0/80/8 P F: 0/80/8 In contrast, Euclidean and DMD failed the test, consistently recording MCC<1MCC<1. DMD recorded MCC=1MCC=1 for only a single DTM generated from NUS, but that instance is trivial. While the other measures exhibit their anti–false edge abilities in SNC, Euclidean and DMD almost always generate at least one false edge. Therefore, these measures were excluded from the subsequent experiments. Outliers. To obtain true fcf_c by removing the topological shielding effect [141], Algorithm 1 requires its input G to be connected. In other words, fcf_c can be overestimated when isolated vertices are removed earlier, even when the actual size of GCG_GC is small. Hence, only four of the 272272 raw SNs were excluded. They were all SNs extracted from the DTM built by using LMRank for SemEval–2017. While the use of MST backbones with l=50l=50 and ω=100ω=100 is sufficient to ensure connected SNs, such corner cases seldom arise when multigrams with sparse co–occurrences are extracted as keyphrases. However, these four outliers were not entirely excluded from the PoC, as further discussed in Section IV. Statistical Analysis. If Algorithm 1 cannot decrease L()L(G) and T△()T_ (G) within h iterations, it returns a mere copy of the SN (G) as its null model nullG_null. As there is no difference between fcempiricalf_c^empirical and fcnullf_c^null, (7) assigns a zero–RI to G. Thus, RI scores of EW measures sometimes follow zero–inflated distributions at the dataset level. Interestingly, certain SNC pipelines are prone to yielding such zero–RI SNs, whose details are further discussed in the qualitative analysis. Indeed, Table XII shows the low average RI scores and high variances. To examine normality, the K–S test and the Shapiro–Wilk (S–W) test were carefully considered but found to be inappropriate (Appendix G). Accordingly, we focused on the Q–Q plots to visually inspect the normality. The Q–Q plots (link) indicated that the normality was clearly violated for 2323 of the 3232 RI distributions. Every 95% BCI (with 10410^4 resamples) of the average RI scores was also wide (link), supporting the non–parametric approach based on rank transformation per distribution (Subsubsection I-C2). TABLE XII: RI–based Evaluation Results (3232 Pairs of Avgs and Stds) Data RI CF Dice Jaccard Cosine Sem10 Avg 0.0150.015 0.0180.018 0.0180.018 0.0420.042 Std 0.0430.043 0.0230.023 0.0230.023 0.0540.054 NUS Avg 0.0000.000 0.0340.034 0.0340.034 0.0560.056 Std 0.0000.000 0.0580.058 0.0580.058 0.0600.060 Inspec Avg 0.0490.049 0.1460.146 0.1460.146 0.1680.168 Std 0.0860.086 0.1280.128 0.1280.128 0.0760.076 KDD Avg 0.0300.030 0.0850.085 0.0850.085 0.1620.162 Std 0.0640.064 0.1250.125 0.1250.125 0.1160.116 W Avg 0.0320.032 0.1140.114 0.1140.114 0.2160.216 Std 0.0570.057 0.1420.142 0.1420.142 0.1260.126 Sem17 Avg 0.0580.058 0.1760.176 0.1760.176 0.2640.264 Std 0.0560.056 0.0760.076 0.0760.076 0.0710.071 DUC21 Avg 0.0510.051 0.1100.110 0.1100.110 0.1250.125 Std 0.0790.079 0.0570.057 0.0570.057 0.0600.060 500N Avg 0.0060.006 0.0460.046 0.0460.046 0.0680.068 Std 0.0160.016 0.0600.060 0.0600.060 0.0760.076 Subsequently, to determine whether significant differences exist among the averages (Table XII), Friedman followed by Nemenyi was performed at the dataset level. Here, a DTM, an EW measure, and a resulting RI score distribution served as a block, a treatment, and a sample, respectively. The number of blocks (i.e., the number of AKE algorithms used) per dataset was small, meaning that each distribution contains only 88 to 1010 observations. As Friedman is prone to Type I errors in such cases [161], we incorporated the Iman–Davenport correction [161] to obtain more reliable p–values. Interestingly, clear significant differences in the average RI ranks (p<0.05p<0.05) were observed only for the short document datasets (Inspec, KDD, W, and SemEval–2017). While Friedman with Iman–Davenport activated the CD diagram for DUC–2001, Nemenyi conservatively tied all measures together by a string (Fig. 14–g). All p–values are provided separately (link) for those seeking further verification. We clarify that SNC ultimately depends on method selection pipelines. Although the presence or absence of statistically significant differences facilitates a better understanding of EW measures, even a marginal numerical difference in RI can be factored into a global SNC pipeline (Subsection IV-D). Maintaining this premise, we provide a post–hoc interpretation. In particular, why did Cosine significantly outperform CF across half of the datasets (Figs. 14–c, d, e, and f)? Qualitative Analysis. Our tentative answer is that while certain SNC pipelines flexibly incorporate contextual information, others rigidly adhere to Co–occurrence Frequency Information (CFI), resulting in differences in RI scores. More specifically, when CF paired with TF was applied to SemEval–2010, a partially star–topological SN, hereafter referred to as a rigid SN, was formed by concentrating edges to a few dominantly co–occurring keyphrases (Fig. 15–a). Most ki∈k_i were also pinned to 11, thereby making edge–rewiring–based Algorithm 1 return a mere copy of the SN (Fig. 15–b). So, zero–RI was yielded (Fig. 15-a). Algorithm 1 precisely prevents such pipelines from obtaining high RI. Figure 14: Critical Difference Diagrams of EW Measures across Datasets. Each value in parentheses is an average of RI ranks across DTMs. Why should we prevent this? Even if we do not demand that EW measures go beyond the level of minimal facet veracity, we can still consider how many facet types each measure can consider. It is also self–evident that any measure that affords a researcher broader room for diverse interpretations is more desirable in terms of abduction. So, we give edge–prioritization opportunities of fair ω to every measure. If certain measures nonetheless adhere to CFI and exhaust ω for dominant keyphrases, thereby diminishing such room, it is karma131313Indeed, when an output remains at its baseline, Output−BaselineMaximum Possible−Baseline Output-BaselineMaximum Possible-Baseline [128] regards the treatment effect as zero (Table VII). that the measures are penalized. Can we, then, observe an actual pattern where CFI–biased EW measures induce zero–RI inflation? Yes. The Sankey diagram [162] in Fig. 16 visualizes which pipelines succeeded or failed in constructing raw SNs with RI>0RI>0 upon completing the EW stage. CF, Dice–Jaccard, and Cosine generated zero–RI SNs in this order. This is a natural outcome, given that CF considers solely CFI, Dice–Jaccard merely adds normalization to CFI (Table IV), and for Cosine, target vectors can be populated with entries that can signify diverse semantics depending on which AKE algorithms it is partnered with. As may be noticed, not only EW measures but also AKE algorithms can serve as relevant factors. For instance, since it was ultimately its partner that passed contextual information to Cosine, when LMRank paired with Cosine was applied to SemEval–2010, a partially mesh–topological SN with RI>0RI>0, hereafter referred to as a flexible SN, was successfully formed. Its many vertices certainly appear to satisfy ki>1k_i>1 (Fig. 15–c). According to Fig. 16, pipelines based on KP–Miner (which uses a strict cutoff), TextRank (which exploits a word co–occurrence binary graph), or N–based algorithms generated fewer zero–RI SNs. In contrast, pipelines based on SingleRank or PositionRank (which exploit word co–occurrence frequency graphs), TF, TF–IDF, or YAKE! generated more zero–RI SNs. Here, an interesting observation is that long document datasets can structurally inject CFI into SNC pipelines. The long document datasets (SemEval–2010 and NUS) contain a large number of tokens, i.e., rich CFI (Table VIII). Indeed, for these datasets, significant differences among the EW measures completely vanished (Figs. 14–a and b). This aligns with Fig. 16, which says that only 34.434.4% (11/3211/32) of pipelines for long–document NUS yielded flexible SNs, whereas short–document SemEval–2017 yielded the most at 97.297.2% (35/3635/36). Figure 15: Cases of Rigid SN (Top) and Flexible SN (Bottom). T and L represent transitivity and the average shortest path length, respectively. TABLE XIII: Results of Spearman’s ρ Correlation Analysis between RI and IP Type X Y Z ρ 9595% BCI with 10410^4 resamples p–value Power General ρ(X, Y)ρ(X, Y) RI IP1IP_1 - 0.9140.914 (0.892,0.929)(0.892,0.929) (3.961×10−141)∗⁣∗(3.961× 10^-141)^*** 1.0001.000 General ρ(X, Y)ρ(X, Y) RI IP2IP_2 - 0.8740.874 (0.841,0.899)(0.841,0.899) (2.762×10−107)∗⁣∗(2.762× 10^-107)^*** 1.0001.000 Partial ρ(X.Z, Y.Z)ρ(X.Z, Y.Z) RI IP1IP_1 IP2IP_2 0.5970.597 (0.496,0.682)(0.496,0.682) (4.337×10−29)∗⁣∗(4.337× 10^-29)^*** 1.0001.000 Partial ρ(X.Z, Y.Z)ρ(X.Z, Y.Z) RI IP2IP_2 IP1IP_1 0.2760.276 (0.138,0.407)(0.138,0.407) (4.094×10−6)∗⁣∗(4.094× 10^-6)^*** 0.9960.996 Nonetheless, document lengths do not solely determine CFI. KDD is a short–document dataset comparable to SemEval–2017, but only 57.557.5% (23/4023/40) of pipelines for KDD yielded flexible SNs. Why? KDD [147] consists of certain abstracts from proceedings of the ACM Conference on Knowledge Discovery and Data Mining (KDD). They share domain–specific terms, i.e., rich CFI. Figure 16: Sankey Diagram of SNC Pipelines. Pipelines with the same outcome are merged into a superpipeline. The red and blue pipelines indicate failures (RI=0RI=0) and successes (RI>0RI>0), respectively. To accommodate colorblind readers, an interactive version of the diagram can be rendered by downloading and executing our code and data (link). In that version, the flow of each pipeline (e.g., TF → CF) can be examined. For any starting point (dataset, AKE algorithm, or EW measure), the collective magnitude of subpipelines that participate in the flow from the point can also be examined. RI Validation. As explained in Subsubsection I-A2, we conducted RI validation. We first conducted the normality test on IP1IP_1, IP2IP_2, and RI for all 268268 raw SNs across the datasets. According to the results of the K–S test (p<0.05p<0.05) and visual inspection of the Q–Q plots (link), normality was not confirmed for any of the variables. Accordingly (cf. Subsubsection I-C2), we conducted Spearman’s ρ analysis [98], with the results presented in Table XIII. Herein, X.ZX.Z [Y.ZY.Z] denotes variable X [Y] after controlling for the effect of Z in X [Y]; p∗⁣∗p^*** indicates that p≤0.001p≤ 0.001, confirming that the null hypothesis of no correlation was clearly rejected. First, the general correlations ρ(RI, IP1)ρ(RI, IP_1) and ρ(RI, IP2)ρ(RI, IP_2) were high at 0.9140.914 and 0.8740.874, respectively, strongly supporting the premise that higher RI aligns with higher IP. Second, the partial correlation ρ(RI.IP2,IP1.IP2)ρ(RI.IP_2,IP_1.IP_2) remained moderate at 0.5970.597, whereas ρ(RI.IP1,IP2.IP1)ρ(RI.IP_1,IP_2.IP_1) was weak at 0.2760.276. That is, the strong general correlation between RI and IP was driven primarily by ρ(RI.IP2,IP1.IP2)ρ(RI.IP_2,IP_1.IP_2) and supplemented by ρ(RI.IP1,IP2.IP1)ρ(RI.IP_1,IP_2.IP_1). Nonetheless, this observed weak ρ(RI.IP1,IP2.IP1)ρ(RI.IP_1,IP_2.IP_1) does not diminish the validity of RI: Although RI rewards smooth semantic percolation, simultaneously maximizing both IP1IP_1 and IP2IP_2 involves an inherent structural trade–off. When hubs cluster, L()L(G) tends to decrease, but because triangles also tend to increase, T△()T_ (G) tends to increase (e.g., small–world networks). Despite this constraint, RI is assigned to SNs satisfying L(null)≥L()L(G_null)≥ L(G) and T△(null)≥T△()T_ (G_null)≥ T_ (G) (Algorithm 1). Therefore, the observed weak ρ(RI.IP1,IP2.IP1)ρ(RI.IP_1,IP_2.IP_1) suggests that certain nontrivial SNs achieved relatively high IP2IP_2 despite this constraint, rather than invalidating the relationship between RI and IP2IP_2. I-E Experiment 3: Community Detection We now report the CD–tailored experimental setup (Subsubsection I-E1) and which of the selected EW measures maximized SN distinctiveness (Subsubsection I-E2). I-E1 Experimental Setup for CD Implementations. We implemented Leiden and the other selected CD algorithms based on Python igraph [163] and NetworkX [164], respectively. Parameters. First, while not detailed earlier, Q has a resolution parameter γ>0γ>0, where higher or lower γ is likely to create more or fewer communities, respectively [118]: Q=12m∑ij[ij−γkikj2m]δ(ci,cj) Q= 12m _ij [A_ij-γ k_ik_j2m ]δ(c_i,c_j) (9) If γ is individually tuned for each SN, the SNs would correspond to different objective functions, rendering a fair comparison impossible. γ is conventionally fixed at 11 to neutralize its influence, a practice followed in this paper. Readers may opt for their own γ in future applications. Second, unlike the original Leiden paper [118], the implementation provided by igraph requires users to specify the number of algorithm iterations. Our informal check based on Optuna [165], a Python library for automated hyperparameter search, indicated that, for most SNs in this PoC, fewer than 200200 iterations were sufficient to reach their maximum Leiden Q. We fixed it at 200200 to save time. Third, the randomness parameter β of Leiden was tuned for each SN by using Optuna. Exploring an extensive range of β with numerous trials per SN is time–consuming. We found that most SNs in this PoC reached maximum Leiden Q within 5050 trials in 0.1≤β≤100.1≤β≤ 10. We selected these time–manageable compromises. I-E2 Results of CD Statistical Analysis. CD was conducted on the 272 raw SNs, including the four outliers that had been excluded at the EW stage. 9595% BCIs of these average Q scores (Table XIV) are provided separately (link). For these 3232 Q distributions (88 datasets times 44 algorithms), while the K–S test indicated that only the FLPA distribution for NUS violated normality, the Q–Q plots of FLPA violated normality across all datasets (link). Accordingly, we decided to maintain the non–parametric approach to ensure consistency in our analysis. TABLE XIV: Summary of 3232 Modularity Q Distributions Data Q CNM Louvain Leiden FLPA Sem10 Avg 0.3120.312 0.3170.317 0.3210.321 0.1170.117 Std 0.0750.075 0.0760.076 0.0750.075 0.1180.118 NUS Avg 0.3480.348 0.3510.351 0.3540.354 0.1620.162 Std 0.0940.094 0.0940.094 0.0940.094 0.1870.187 Inspec Avg 0.4020.402 0.3980.398 0.4080.408 0.2280.228 Std 0.1240.124 0.1230.123 0.1230.123 0.1960.196 KDD Avg 0.3460.346 0.3490.349 0.3530.353 0.1980.198 Std 0.1350.135 0.1360.136 0.1340.134 0.1830.183 W Avg 0.3910.391 0.3880.388 0.3940.394 0.2450.245 Std 0.1300.130 0.1300.130 0.1300.130 0.2070.207 Sem17 Avg 0.4290.429 0.4310.431 0.4380.438 0.2580.258 Std 0.1050.105 0.1050.105 0.1040.104 0.1980.198 DUC21 Avg 0.4290.429 0.4300.430 0.4350.435 0.2940.294 Std 0.1780.178 0.1790.179 0.1760.176 0.2740.274 500N Avg 0.4060.406 0.4060.406 0.4100.410 0.3030.303 Std 0.1270.127 0.1310.131 0.1290.129 0.1930.193 Figure 17: Critical Difference Diagrams of CD Algorithms across Benchmark Datasets. Each value in parentheses is an average of Q ranks across SNs. To determine whether significant differences exist among the average Q ranks, Friedman followed by Nemenyi was performed at the dataset level. A raw SN, a CD algorithm, and a resulting Q score distribution corresponded to a block, a treatment, and a sample, respectively. For all datasets, Friedman indicated that significant differences in the average Q ranks existed among at least one pair of CD algorithms (p<0.05p<0.05). Nemenyi then identified which pairs exhibited significance at the dataset level (Fig. 17). All p–values have been disclosed separately (link) for brevity. Qualitative Analysis. Based on the significant differences (p<0.05p<0.05) shown in Fig. 17 and the statistics in Table XIV, we provide the following post–hoc interpretation. First, the average Q scores followed the descending order of Leiden, Louvain, CNM, and FLPA across most datasets (Table XIV). These results were as expected, given that the heuristic–based FLPA did not explicitly optimize Q, whereas the other three algorithms followed the incremental advancement path of modularity–based algorithms. Second, however, no significant differences in average Q ranks were observed between Louvain and CNM, the middle–tier algorithms (Fig. 17). Even for a few datasets (Inspec, W, and 500N–KP–Crowd), CNM’s greedy optimization surpassed Louvain’s approach in terms of average Q scores, though the differences were marginal (Table XIV). This lack of distinction likely stemmed from the sparsity of vertex adjacency information and edge weight information, as the size of each SN was small (l=50l=50 and ω=100ω=100). Algorithms capable of maximizing an objective function even under such information scarcity can be prioritized for future applications. IV Global Optimization In this section, Subsection IV-A first answers RQ7 (“How are local evaluation results across the SNC stages integrated to identify the optimal SN?”). To answer upfront, the results are integrated by reformulating SNC as a Process Optimization Problem (POP) and factoring the results into a global objective function J. Here, an SNC process that maximizes J is regarded as the optimal policy (or pipeline) that generates the optimal SN for a textual dataset. However, providing J in isolation may pose challenges for its reuse. Thus, Subsection IV-B presents the comprehensive framework ClueNetwork, which incorporates all the key components ((1), (2), l, ω, Algorithm 1, hF1hF_1, RI, a CSF, the veracity pretest, and J). As such, ClueNetwork facilitates ranking candidate policies (ultimately their resulting SNs) for a dataset. Of course, Subsection IV-C answers RQ8 (“How is J defined and justified?”), thereby establishing the framework’s core, J, not as a mere heuristic, but as a scientifically realistic criterion. Only after that does Subsection IV-D finalize the PoC of ClueNetwork by demonstrating that it is an actually working framework through an ablation study. IV-A Problem Reformulation Semantic Network Construction (SNC) is a Process Optimization Problem (POP). A POP can be regarded as a problem divided into multiple stages, each requiring a decision [166, 167]. Specifically, the current iith stage takes one of its possible states (si∈i=si,1,si,2,…,si,|i|) (s_i _i=\s_i,1,s_i,2,…,s_i,|S_i|\ ) associated with a decision (xi−1x_i-1) at the previous (i−1)(i-1)th stage. Then, a decision at the current stage (xi∈i=xi,1,xi,2,…,xi,|i|) (x_i _i=\x_i,1,x_i,2,…,x_i,|X_i|\ ) transitions the current state (sis_i) into a state (si+1s_i+1) at the subsequent (i+1)(i+1)th stage. Figure 18: SNC for a Given Dataset. SNC precisely follows this structure. That is, the selections of an AKE algorithm (x1x_1), EW measure (x2x_2), and CD algorithm (x3x_3) at the first, second, and third stages determine a DTM (s2s_2), raw SN (s3s_3), and final SN (s4s_4). Such selections yield function values hF1(x1)hF_1(x_1), RI(x2)RI(x_2), and Q(x3)Q(x_3). Accordingly, components of SNC can be reformulated as follows: • 1S_1: Set of textual datasets in the world. • s1s_1: Given dataset, where s1∈1s_1 _1. • 1X_1: Set of given AKE algorithms. • x1x_1: Selected algorithm, where x1∈1x_1 _1. • cs1,x1=(average) hF1(x1)c_s_1,x_1=(average) hF_1(x_1): Confidence for SN keyness obtained by applying x1x_1 to s1s_1. • 2S_2: Set of DTMs (|2|=|1|) (|S_2|=|X_1| ). • s2s_2: Given DTM, where s2∈2s_2 _2. • 2X_2: Set of given veracious EW measures. • x2x_2: Selected measure, where x2∈2x_2 _2. At this point, we clarify that zero–RI SNs and unconnected SNs (e.g., the four outliers mentioned in Subsubsection I-D2) should not be excluded from SNC. Although they exhibit no observable effects (i.e., RI scores) in terms of SN interpretability, they are also built by using EW measures that pass the (minimal) veracity pretest. Hence, it is fair to assign them the same baseline score of 11 for SN veracity by separating the dimension of veracity from that of interpretability. That is, RI scores should be treated as additional points. • cs2,x2=(1+RI(x2))/2c_s_2,x_2= (1+RI(x_2) )/2: Confidence for the overall quality (veracity and interpretability) of interactions between keyphrases in an SN obtained by applying x2x_2 to s2s_2. Herein, cs2,x2c_s_2,x_2 is calculated as the average of the baseline score (i.e., 11) and the actual RI score (0≤RI≤10 ≤ 1). Then, • 3S_3: Set of raw SNs (|3|=|1|×|2|) (|S_3|=|X_1|×|X_2| ). • s3s_3: Given raw SN, where s3∈3s_3 _3. • 3X_3: Set of given CD algorithms. • x3x_3: Selected algorithm, where x3∈3x_3 _3. • cs3,x3=Q(x3)c_s_3,x_3=Q(x_3): Confidence for SN distinctiveness obtained by applying x3x_3 to s3s_3. • 4S_4: Set of final SNs (|4|=|1|×|2|×|3|) (|S_4|=|X_1|×|X_2|×|X_3| ). • s4s_4: Constructed final SN, representing a terminal state. • si→xisi+1s_i x_is_i+1: Deterministic move to a subsequent state si+1s_i+1 resulting from taking xix_i at the current state sis_i. In the fields of operations research [167] and reinforcement learning [168], xix_i, csi,xic_s_i,x_i, and si→xisi+1s_i x_is_i+1 are termed an “action (or decision),” a “reward,” and a “transition,” respectively. In terms of SNC, the goal is to identify the optimal policy (the sequence of selected actions that jointly maximizes a global confidence in the optimality of a final SN for a given dataset). • : Set of possible policies, where ||=|4|| |=|S_4|. • π=(x1,x2,x3)π=(x_1,x_2,x_3): Policy (process or pipeline), which is a specific combination of an AKE algorithm (x1x_1), EW measure (x2x_2), and CD algorithm (x3x_3), where π∈π∈ . • π∗=(x1∗,x2∗,x3∗)π^*=(x_1^*,x_2^*,x_3^*): Optimal policy, which is the sequence of selected actions that jointly maximizes a global confidence for SN optimality, where π∗∈π^*∈ . Here, to identify π∗π^* for a given dataset, information regarding possible rewards at each stage is required. Hence, • iC_i: Set of rewards at the iith stage, where csi,xi∈ic_s_i,x_i _i. Global Objective Function. Based on these components, we can reformulate a joint confidence for SN optimality as a global objective function: MaximizeJ(π)=∏i=13csi,xi=cs1,x1×cs2,x2×cs3,x3, J(π)= _i=1^3c_s_i,x_i=c_s_1,x_1× c_s_2,x_2× c_s_3,x_3, (10) wherecs1,x1=hF1(x1)cs2,x2=1+RI(x2)2cs3,x3=Q(x3), , subject to0≤csi,xi≤1,∀i∈1,2,3. to 0≤ c_s_i,x_i≤ 1,\;\ ∀\;\ i∈\1,2,3\. This multiplicative expression links the local confidences like a chain. ClueNetwork regards some π maximizing this expression as the optimal policy π∗π^* that yields the optimal SN. Here, one can demand, • “Why do we multiply cs1,x1c_s_1,x_1, cs2,x2c_s_2,x_2, and cs3,x3c_s_3,x_3? Provide criteria for the optimal SN and evidence that the current expression of J harmonizes with them, thereby demonstrating that a higher J guarantees a better SN.” Legitimate, and we will do so in Subsection IV-C. Nonetheless, let us first present ClueNetwork under the assumption that J is somehow justified. IV-B ClueNetwork IV-B1 Framework ClueNetwork is presented in Fig. 19. Due to the figure’s unavoidable large size and placement, we respectfully encourage readers to view this PDF side–by–side by displaying the figure in one window and this main text in the other. Stage 1 (AKE). First, as previously emphasized, an AKE algorithm is an ensemble of its preprocessing strategy, itself, and its parameters. Algorithms given independently perform AKE on a given dataset depending on their philosophies of keyness. Here, certain algorithms require postprocessing. Why? The point is that both gold keyphrases and scored terms should be stemmed (e.g., “definition(s)” →stemming stemming “defin” ) to ensure a consistent hF1hF_1–based evaluation. For instance, N–based algorithms cannot extract appropriate contextual embeddings from stemmed forms (i.e., lexical forms). Hence, they first obtain embeddings and keyness scores for surface forms, and then perform poststemming. Thereafter, if multiple surface forms share the same stemmed form, only the stemmed form becomes a candidate, and its keyness score is determined as that of the surface form with the highest keyness score (or earliest offset). Second, each algorithm’s average hF1hF_1 across all documents is recorded into a score dataframe (please refer to the “Artifacts’ Domain” in Fig. 19), and each returns a ∈ℝm×nDTM ^m× n. Third, every row of each DTM is normalized by using (1). Fourth, each dimension–reduced new DTM ∈ℝm×l ^m× l is obtained by calculating final candidate scores based on (2) and applying the resolution parameter l. Stage 2 (EW). The obtained DTMs are utilized in two ways. First, they serve as references for the minimal veracity pretest on given EW measures. Second, only measures that have passed the test are allowed to focus on different facets of every DTM to return TTMs ∈ℝl×l ^l× l. Given that users might conceive flawed hypotheses without the pretest as a safeguard, the provision of the pretest constitutes ClueNetwork’s touch of novelty. Third, MSTs are built by applying established Kruskal’s algorithm [143] to the TTMs. Fourth, the MSTs serve as backbones of raw SNs — each raw SN is built by sequentially adding higher–weighted TTM entries to the corresponding MST until the total number of edges reaches ω. Fifth, raw SNs are evaluated via vertex random failure simulation and RI analysis, and then resulting RI scores are restored into the score dataframe. Given that users would otherwise have to prepare elusive gold edge weights without this evaluation mechanism, it also constitutes ClueNetwork’s touch of novelty. Stage 3 (CD). First, selected CD algorithms are applied to the raw SNs, thereby obtaining final SNs. The final SNs are stored in a dictionary, where the keys are identifiers representing configurations of SNC pipelines (e.g., (LMRank, Cosine, Leiden)) and the values are corresponding final SNs. Second, the final SNs are evaluated by a CSR, and then their resulting scores are stored in the score dataframe. Figure 19: Workflow of ClueNetwork. For detailed descriptions, please refer to the main text. Global Optimization. After all local evaluations have been completed, the framework integrates them into an exhaustive search mechanism for the optimal SN. First, if the local evaluation results have appropriately accumulated into the score dataframe D, it resembles Table XV. TABLE XV: Conceptual Illustration of Score Dataframe D. x1x_1 x2x_2 x3x_3 cs1,x1c_s_1,x_1 cs2,x2c_s_2,x_2 cs3,x3c_s_3,x_3 TF CF CNM (…) (…) (…) TF CF Louvain (…) (…) (…) TF CF Leiden (…) (…) (…) TF CF FLPA (…) (…) (…) TF–IDF CF CNM (…) (…) (…) ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ LMRank Cosine Leiden (…) (…) (…) LMRank Cosine FLPA (…) (…) (…) Second, such cs1,x1c_s_1,x_1, cs2,x2c_s_2,x_2, and cs3,x3c_s_3,x_3 columns in Table XV serve as 1C_1, 2C_2, and 3C_3. The element–wise product of 1C_1, 2C_2, and 3C_3, produces a column J containing all J(π)J(π) scores. Third, by appending J to D and then sorting D in descending order, π∗π^* and J(π∗)J(π^*) from the top row are identified. The auxiliary Algorithm 2 summarizes these steps. Finally, the identified π∗π^* is used as the key to retrieve the corresponding optimal SN from the final SN dictionary. Input: D Output: π∗π^* and J(π∗)J(π^*) ⊳ Main Steps :=1⊙2⊙3J:=C_1 _2 _3, where D includes i∈1,2,3C_i∈\1,2,3\ Update D by appending J Sort D in descending order based on J Identify the top row in D Regard (x1,x2,x3)(x_1,x_2,x_3) from the top row as π∗π^* Regard J(π)J(π) from the top row as J(π∗)J(π^*) return π∗π^* and J(π∗)J(π^*) Algorithm 2 Auxiliary Algorithm Vertex Label Correction. The steps described can be readily implemented by anyone possessing standard programming skills. Consequently, ClueNetwork can be readily reused. Nonetheless, there is a noteworthy consideration. As previously explained, candidate terms in the AKE stage are compared with gold keyphrases in their stemmed forms. Since such stemmed forms are preserved throughout the subsequent stages (cf. Fig. 15), vertex labels of an identified optimal SN should be corrected from stemmed forms to corresponding surface forms to ensure interpretability. How? During preprocessing in AKE, a container, such as the PKE toolkit’s Candidate container141414The conceptualization of such a container may be aided by Lines 208–235 in this script (link) and Lines 30–49 in this script (link)., that maps each stemmed form (i.e., lexical form) to its corresponding list of surface forms can be built. Thereafter, the optimal SN’s stemmed–form vertex labels are used as keys to retrieve corresponding surface forms from the container, thereby correcting the labels. Since AKE algorithms independently perform preprocessing, such containers should be created and managed separately for each algorithm. IV-B2 Handling Lack of Gold Keyphrases Here, one might ask, “Okay, you have presented a framework. But how can I obtain hF1hF_1 scores for any AKE algorithm when my dataset lacks gold keyphrases?” A timely question. Most textual datasets, unless they consist of academic papers with author keywords, can lack gold keyphrases. However, there exist at least two practical solutions, although we defer them to future applications (given the scope and length constraints): If You Can Be Experts, Then the Experts Can Be Gold Standards. The notion that persons possessing expertise on certain targets can annotate them has been accepted in the field of KR [35]. So, a research team can also first sample a subset of documents from a dataset. The team can read each document, simultaneously becoming its experts, and then annotate it with multi–annotator validation. While an ideal sample size can vary depending on the data, it should significantly exceed 3030 (the minimum size required for the Central Limit Theorem to hold), given that an average hF1hF_1 obtained from such a sample is an algorithm’s cs1,x1 c_s_1,x_1. Silver Keyphrases. For a researcher without a team who finds manual annotation burdensome, leveraging a SOTA LLM with appropriate prompts can be considered to automatically assign silver keyphrases to documents [169]. This solution is also powerful because such an LLM facilitates annotation for an entire dataset beyond a small sample. However, the solution requires meta–evaluation of whether silver keyphrases can truly represent reality. Furthermore, if the backbone of a participating N–based algorithm and the annotator LLM are contextually close, the competition can be biased. Notwithstanding these considerations, it remains a promising solution given recent advancements in NLP. IV-C Justification of J Let us now respond to the previously deferred demand, “Provide criteria for the optimal SN and evidence that the current expression of J harmonizes with them.” Here, Subsubsection IV-C2 provides a theoretical response, “In fact, the current J itself is the very criterion, and J already not only harmonizes with but also coincides with the criterion. This is not circular reasoning.” Nonetheless, some peers might not accept this response. So, Subsubsection IV-C3 empirically demonstrates through perturbation analysis that the current J harmonizes with reality more than additive expressions, such as weighted sum or simple average. Before these responses, Subsubsection IV-C1 rules out irrelevant expectations by clarifying which approaches are unsuitable for this justification. IV-C1 Unsuitable Justification Approaches Gold–SN–Based Approaches. Throughout this paper, we have already shown that gold SNs remain elusive — specifically, here (link) and here (link). Just as planets with countless diamonds far more valuable than gold might exist yet remain inaccessible to us, we no longer consider gold SNs. Human Judgments. Likewise, we do not recruit experts or undergraduate students and ask them to judge qualities of SNs extracted by using J. It is highly labor–intensive and makes our already thin wallets even thinner. Hypothesis–Testing–Based Approaches. Given that this paper is not a social science study, we do not derive hypotheses from SNs and test them. We have already clarified that, unlike KGs, SNs as clues are not collections of propositions (link). Therefore, the veracity of hypotheses derived from SNs must be decoupled from qualities of the SNs themselves. Extrinsic Approaches. Sometimes, we also serve as peer reviewers and encounter papers that justify their frameworks using extrinsic approaches. Here, while we say, “Congratulations. Your frameworks happen to align well with extrinsic tasks” to authors whose frameworks perform well on such tasks, we do not simply say, “Your papers should be rejected” to authors whose frameworks perform poorly on them. Why? While the Platonic Representation Hypothesis [170] argues that, as AIs advance, their representations appear to converge toward the Forms (?!) of vector representations, the recently proposed Aristotelian151515Understanding why Aristotle appears here requires an understanding of his metaphysics [172], certainly beyond the scope. It suffices to know that, whereas Plato regarded fixity as the condition of being, Aristotle did not (i.e., the banana mentioned here (link) also existed) [172]. view [171] suggests that AIs’ representations are only converging toward shared local neighborhood relationships rather than a globally shared geometry. Likewise, justifying J based on performance obtained by sharing SN representations to extrinsic representation–based systems seems to involve both luck and mismatch, given the possible absence of a globally shared geometry. Therefore, extrinsic task performance may not directly measure qualities of J–driven SNs themselves. IV-C2 Theoretical Justification: Bayesian Perspective Decision–making Under Uncertainty. Let us begin with the fact that this paper’s notion of optimal SN has consistently been confined to an SN that achieves the highest joint confidence for the local objectives (link). Also, let us acknowledge the fact that, for any textual dataset, any expression of J operates under “uncertainty” about which SN actually represents it, yet J must decide on the most “desirable” (in our terminology, “optimal”) SN, while whether that decision actually corresponds to reality remains “uncontrollable” [173]. Subjective Probabilities. Hence, what any J ultimately incorporates into its expression is a set of subjective probabilities concerning an SN. And de Finetti, one of the proponents of Bayesian statistics, defined subjective probability as [174]: • “the degree of belief, attributed by a given person at a given instant and with a given set of information, in the occurrence of an event.” Therefore, if “instant,” “person,” “set of information,” and “event” herein can be defined in terms of SNC, we can also define subjective probabilities for the optimal SN: • Instant: si∈is_i _i, where i∈2,3,4i∈\2,3,4\. • Person: a “putative” [9] rational peer reviewer that evaluates whether a given SN has achieved [keyness, interpretability, or distinctiveness]. • Set of Information: csi,xic_s_i,x_i ∈χ|χ∈\χ|χ is known to the person\. • Event: ℰiE_i and ℰicE_i^c, the events that the SN has achieved or not achieved [keyness, interpretability, or distinctiveness], respectively, where ℰi,ℰicE_i,E_i^c ⊊ Ωi _i, the sample space, and Ωi=achieved, not achieved _i=\ achieved, not achieved\. Then, would the rational reviewer evaluate the subjective probabilities based on irrelevant information, such as average prices of the reviewer’s breakfast, lunch, and dinner? Certainly not. The reviewer would evaluate them based on the obtained relevant scores (cs1,x1c_s_1,x_1, cs2,x2c_s_2,x_2, and cs3,x3)c_s_3,x_3) of the local objectives (SN keyness, interpretability, and distinctiveness). That is, the subjective probabilities can be formulated as: cs1,x1,cs2,x2,and cs3,x3⟶can be treated asP(ℰ2),P(ℰ3∣ℰ2), and P(ℰ4∣ℰ2∩ℰ3), respectively. gatheredc_s_1,x_1,\;c_s_2,x_2,\;and \;c_s_3,x_3\\[2.0pt] can be treated as \\[2.0pt] P(E_2),P(E_3 _2), and P(E_4 _2 _3), respectively. gathered (11) Subjective Probabilities Are All J Can Say. As de Finetti clarifies [175], such subjective probabilities acknowledge that uncertain things are uncertain, rather than directly making assertions about reality. Indeed, there is little else that any J can represent concerning SNs beyond P(ℰ2)P(E_2), P(ℰ3∣ℰ2)P(E_3 _2), and P(ℰ4∣ℰ2∩ℰ3)P(E_4 _2 _3). Nevertheless, these are “the criteria for the optimal SN.” Why? Because, insofar as a J systematically incorporates cs1,x1c_s_1,x_1, cs2,x2c_s_2,x_2, and cs3,x3c_s_3,x_3 to represent relevant evaluation results, an SN selected based on J should be regarded as the rational, and thereby optimal, SN. Then, Why Do We Multiply Them? P(ℰ2)P(E_2), P(ℰ3∣ℰ2)P(E_3 _2), and P(ℰ4∣ℰ2∩ℰ3)P(E_4 _2 _3) are local confidences (degrees of belief) in different aspects of an SN. What we ultimately need is a joint confidence in their joint artifact. Then, the “putative” [9] rational reviewer would treat this global confidence as given by (12)–b concerning the joint sample space defined in (12)–a, in which case J can also be re–expressed as (12)–c: Ω=Ω2×Ω3×Ω4⋯(a) = _2× _3× _4·s(a) (12) J=cs1,x1×cs2,x2×cs3,x3⟶can also be treated as J=c_s_1,x_1× c_s_2,x_2× c_s_3,x_3 can also be treated as P(ℰ2∩ℰ3∩ℰ4)=P(ℰ2)P(ℰ3|ℰ2)P(ℰ4|ℰ2∩ℰ3)⋯(b) P(E_2 _3 _4)=P(E_2)P(E_3|E_2)P(E_4|E_2 _3)·s(b) maxJ(π)=maxP(ℰ2∩ℰ3∩ℰ4∣π)⋯(c) π J(π)= π P(E_2 _3 _4 π)·s(c) In short, the reason we multiply P(ℰ2)P(E_2), P(ℰ3∣ℰ2)P(E_3 _2), and P(ℰ4∣ℰ2∩ℰ3)P(E_4 _2 _3) is that doing so logically follows from the established chain rule of probabilities. Conditions of Coherence. One may point out that the fact that cs1,x1c_s_1,x_1, cs2,x2c_s_2,x_2, cs3,x3c_s_3,x_3, and J are relevant to SNC is insufficient, by itself, to make it rational to treat them as P(ℰ2)P(E_2), P(ℰ3∣ℰ2)P(E_3 _2), P(ℰ4∣ℰ2∩ℰ3)P(E_4 _2 _3), and P(ℰ2∩ℰ3∩ℰ4)P(E_2 _3 _4), respectively. Indeed, de Finetti clarifies that, for anything to qualify as a subjective probability, it must also satisfy coherence, formalized by the following conditions [175]: • Boundedness: 0≤P(ℰi)≤10≤ P(E_i)≤ 1. • Normalization: P(Ωi)=1P( _i)=1. • Finite Additivity: P(⋃j=1nℰi,j)=∑j=1nP(ℰi,j)P( _j=1^nE_i,j)= _j=1^nP(E_i,j), where ℰi,j∩ℰi,k=∅ (j≠k)E_i,j _i,k= (j≠ k) and n=|possible ℰi,j|<∞n=|\possible E_i,j\|<∞. Here, these conditions express the requirement that probabilities evaluated by a person for events in an event set must not contradict one another; de Finetti explains that, if any person wishes to avoid “decisions whose consequences are manifestly undesirable (leading to certain loss)” [175], these conditions must be satisfied. Readers interested in cases of such irrational decisions that de Finetti demonstrates as resulting from violations of these conditions may consult [176]. De Finetti opposes constraints beyond these conditions because doing so is prone to excluding valid evaluations of probabilities as invalid [174]. Accordingly, for cs1,x1c_s_1,x_1, cs2,x2c_s_2,x_2, cs3,x3c_s_3,x_3, and J, which constitute the criteria for SNC, to function as starting points for supporting exploratory research, satisfying these conditions alone is theoretically sufficient. Then, do these criteria satisfy these conditions? Demonstration. Yes. First, cs1,x1c_s_1,x_1 (cf. Table VI) and cs2,x2c_s_2,x_2 (cf. (7)) range from 0 to 11 and thus automatically satisfy boundedness. Although Modularity Q originally ranges from −1-1 to 11 [21, 24], under the nonnegativity constraint in (10), negative Q values are truncated at zero. That is, cs3,x3c_s_3,x_3 is given by max⁡Q(s4),0 \Q(s_4),0\ and thus satisfies boundedness. Second, for any csi,xic_s_i,x_i, Ωi _i is achieved, not achieved\ achieved, not achieved\ and values (csi,xic_s_i,x_i and 1−csi,xi1-c_s_i,x_i) assigned to these two mutually exclusive events always sum to 11. Therefore, any csi,xic_s_i,x_i satisfies both normalization and finite additivity. Third, therefore, cs1,x1c_s_1,x_1, cs2,x2c_s_2,x_2, and cs3,x3c_s_3,x_3 can be treated as P(ℰ2)P(E_2), P(ℰ3∣ℰ2)P(E_3 _2), and P(ℰ4∣ℰ2∩ℰ3)P(E_4 _2 _3), respectively, and thus J necessarily not only satisfies boundedness, normalization, and finite additivity but, from the chain rule of probabilities, can also be treated as P(ℰ2∩ℰ3∩ℰ4)P(E_2 _3 _4). Finally, therefore, our theoretical response to the demand to “Provide criteria for the optimal SN and evidence that the current J harmonizes with them” is as follows: “cs1,x1c_s_1,x_1, cs2,x2c_s_2,x_2, cs3,x3c_s_3,x_3, and the current J themselves are the very criteria, and J already not only harmonizes with but also coincides with the criteria. This is not circular reasoning. Rather, it is a logically necessary consequence from the Bayesian perspective.” De Finetti’s Counterarguments to Calibrationists. Here, one might ask, “Okay, the current J is theoretically coherent. But would it be unscientific if actual evidence that J harmonizes with reality still has not been provided?” De Finetti would probably say no. Why? The claim that the scientific legitimacy of subjective probabilities should be grounded in empirical evidence presupposes that objective probabilities are inherent in reality. De Finetti points out that there is no evidence for such a presupposition, as what we actually observe is events and their frequencies, whereas probability is an additional concept161616This is why de Finetti consistently speaks not of discovering probabilities, but of evaluating probabilities [173]–[176]. introduced by human beings [173]. One might nevertheless press the point, “Apart from petitio principii (begging the question) involved in the presupposition, could some actual reviewers not construct J as other expressions, such as a weighted sum? If so, values of the current J would differ from empirically obtained J values. In that case, the current J would need to be calibrated.” That is, one would then have us submit our 1,088 SNs to this IEEE Access journal and ask Reviewers #1 through #32640171717Why 32,640? Reviewers for each SN should significantly exceed 3030, as a conventional rule of thumb for invoking the Central Limit Theorem. to evaluate their qualities on a scale from 0 to 11. Apart from its impracticality, de Finetti would probably point out that such calibration is not constitutive of J itself. Why? As de Finetti explains [176]: a subjective probability is a prior (yet rational) evaluation of an event based on information available under uncertainty, but it is not a prediction about the future outcome. Once the outcome becomes known (once uncertainty is removed), information is updated, and so a posterior evaluation can arise. It is therefore an error categoriae (category mistake) to judge the prior evaluation based on the posterior evaluation. In short, J does not assert any proposition, yet represents a rational belief. In other words, calibration is useful, yet J concerns starting points, not endpoints, in science. IV-C3 Empirical Justification: Perturbation Analysis To Avoid Re–Re–Revision. Nonetheless, might some reviewers still not accept the Bayesian perspective, or that of de Finetti? If so, this paper could be rejected again, which is certainly not what we want. Fortunately, although it is difficult to show that “the current J aligns with truth,” showing that “it conflicts with falsehood” is easy. Furthermore, under a well–designed perturbation analysis, these two are logically equivalent. Please consider the following. Comparative Expressions of J. First, we decided to confirm whether J should indeed take its current multiplicative form. We conducted a perturbation analysis on the current form as well as alternative forms in which J was modified into general weighted sum forms. Here, the simple average (arithmetic mean), Inverse–Variance Weighting (IVW) method [177], and CRITIC (CRiteria Importance Through Intercriteria Correlation) method [178] were employed as weighting methods. Although these methods differ in detail (Table XVI), in terms of SNC, they fundamentally share an optimistic perspective that a loss in one stage can be compensated to some extent by another. This sets them apart from our J, which penalizes global confidence in SN optimality if a local objective is not sufficiently met in even a single stage. TABLE XVI: Weight Formulas Tailored to Our Perturbation Analysis Method Weight wiw_i of csi,xic_s_i,x_i Philosophy Arithmetic Mean 1/31/3 The three criteria are equally important. IVW 1/σi2∑j=131/σj2 1/σ^2_i _j=1^31/σ^2_j More stable criteria are given greater weight. CRITIC σi∑j=13(1−ρij)∑k=13[σk∑j=13(1−ρkj)] _i _j=1^3(1- _ij) _k=1^3 [ _k _j=1^3(1- _kj) ] More discriminative and less redundant criteria are given greater weight. For a given textual dataset, σi2 _i^2 is the variance of applied SNC pipelines’ csi,xic_s_i,x_i values; ρij _ij is Spearman’s ρ between distributions of csi,xic_s_i,x_i and csj,xjc_s_j,x_j. Perturbation Analysis Procedure was as follows. First, the SNC pipelines (KP–Miner, Cosine, Leiden) for NUS and (KeyBERT, Cosine, Leiden) for SemEval–2017 served as targets. For brevity while maintaining generalizability, these optimal pipelines (cf. Table XVII) for the long–document dataset (NUS) and short–document dataset (SemEval-2017) were chosen. Second, a unit of noise consisted of injections across respective stages. Specifically, for the SN corresponding to a target pipeline, its one vertex label (and its occurrences in the sets of prioritized keyphrases) were replaced with a dummy label Frog#X (i.e., Frogs#1, #2, …, and #50); a (possibly distinct) vertex was removed; and (possibly) another vertex was returned to a single community. Figure 20: Global Perturbation Analysis Results for NUS. Third, under these conditions, cs1,x1c_s_1,x_1, cs2,x2c_s_2,x_2, cs3,x3c_s_3,x_3, and J were measured across all competing forms of J. Fourth, by repeating these steps for all l=50l=50 vertices, we obtained the normalized perturbation response trajectories (Figs. 20 and 21). The implementations have been disclosed separately (link 1, link 2). Herein, the y–axis denotes values of J(k)/J(0)J(k)/J(0), where J(k)J(k) and J(0)J(0) represent J when k units of noise were injected and the baseline J without noise, respectively. Figure 21: Global Perturbation Analysis Results for SemEval–2017. Our J Reacted More Strongly Against False Information. Such noise is certainly false. It replaces keyphrases with out–of–conext frogs, deceives an SN interpreter by rendering available hubs unusable, and forcibly isolates vertices that belong to certain communities. Therefore, there is no room for a third property or intermediate state analogous to “gray between black and white” or “0.50.5 between 0 and 11.” Only mutually contradictory truth and falsehood exist as options. At this crossroads, if there is a form of J that rejects falsehood more strongly, the only remaining logical possibility is to believe that it aligns with reality better than the others. Our J was precisely this form, as shown in Figs. 20 and 21. Local Implications. For the sake of academic honesty and for potential users of ClueNetwork, we also share findings (Table XVII) that are unwelcome to us, even if they are not central to the subject matter. Herein, a relative drop rate is defined as y(0)−y(50)y(0)×100% y(0)-y(50)y(0)× 100\%, where y(0)y(0) and y(50)y(50) are values of a metric y without noise and with maximum noise, respectively: TABLE XVII: Brief Ablation Study via Relative Drop Rate Analysis Configuration (Metric) Relative Drop Rate (%) AKE (cs1,x1c_s_1,x_1) 3.04%3.04\% EW (cs2,x2c_s_2,x_2) 14.67%14.67\% CD (cs3,x3c_s_3,x_3) 100.00%100.00\% Only with out AKE (cs2,x2×cs3,x3c_s_2,x_2× c_s_3,x_3) 100.00%100.00\% Only with out EW (cs1,x1×cs3,x3c_s_1,x_1× c_s_3,x_3) 100.00%100.00\% Only with out CD (cs1,x1×cs2,x2c_s_1,x_1× c_s_2,x_2) 17.27%17.27\% Full (cs1,x1×cs2,x2×cs3,x3c_s_1,x_1× c_s_2,x_2× c_s_3,x_3) 100.00%100.00\% As shown in Table XVII, our J’s impressive anti–false performance was primarily driven by CD, whereas EW and AKE contributed minimally. This is because Q is a metric that directly measures the partition quality of a given SN, whereas hF1hF_1 measures the general prioritizing ability of an applied AKE method, and RI does not function independently, but rather forms cs2,x2c_s_2,x_2 together with the baseline score. These local criteria were certainly chosen under limited resources. However, this result leaves the open question of which local criteria should serve as proxies for our belief in SN optimality. Nevertheless, we clarify that this result reflects the inherent difficulty of selecting local criteria, rather than a structural flaw of our J itself. IV-D Ablation Study The culmination of a PoC for any framework lies in demonstrating that it actually works. Hence, we conducted an illustrative ablation study (link) using ClueNetwork. The conventional SNC pipeline (TF – CF – Louvain) was first selected as the baseline. Subsequently, for each dataset, we evaluated the extent of global confidence improvement in SN optimality by comparing the objective function value of the baseline with that of the optimal SNC process. The results are summarized in Table XVIII, where “⇒ ” denotes a method substitution. We provide the following post–hoc interpretation for Table XVIII. First, the optimal processes outperformed the baseline across all datasets. That is, ClueNetwork actually worked. The overall low J values merely reflect the intrinsic difficulty of SNC. Second, for most datasets except for 500N–KP–Crowd, simply replacing TF with the AKE algorithms of the optimal processes resulted in relative J increases over the baseline, ranging from 61.78%61.78\% to 527.08%527.08\%. Given that well–extracted keyphrases enhance confidence for SN optimality, researchers should strive to start on the right foot. TABLE XVIII: Results of Ablation Study Across Benchmark Datasets. The optimal solutions were identified by ClueNetwork. Dataset SNC Process (also termed Pipeline or Policy) cs1,x1c_s_1,x_1 cs2,x2c_s_2,x_2 cs3,x3c_s_3,x_3 J ΔJ J (ΔJ/Jbaseline)( J/J_baseline) ×100%× 100\% SemEval–2010 TF – CF – Louvain (Baseline) 0.1340.134 0.5000.500 0.3660.366 0.0250.025 - - ++ TF ⇒ KP–Miner 0.2870.287 0.5600.560 0.3000.300 0.0480.048 +0.024+0.024 +96.70%+96.70\% ++ CF ⇒ Cosine 0.2870.287 0.5300.530 0.4710.471 0.0720.072 +0.047+0.047 +191.31%+191.31\% ++ Louvain ⇒ Leiden (Optimal) 0.2870.287 0.5300.530 0.4730.473 0.0720.072 +0.047+0.047 +192.87%+192.87\% NUS TF – CF – Louvain (Baseline) 0.1440.144 0.5000.500 0.3190.319 0.0230.023 - - ++ TF ⇒ KP–Miner 0.3410.341 0.5000.500 0.2180.218 0.0370.037 +0.014+0.014 +61.78%+61.78\% ++ CF ⇒ Cosine 0.3410.341 0.5860.586 0.5640.564 0.1130.113 +0.090+0.090 +390.01%+390.01\% ++ Louvain ⇒ Leiden (Optimal) 0.3410.341 0.5860.586 0.5640.564 0.1130.113 +0.090+0.090 +390.01%+390.01\% Inspec TF – CF – Louvain (Baseline) 0.1250.125 0.5000.500 0.2500.250 0.0160.016 - - ++ TF ⇒ LMRank 0.3640.364 0.6220.622 0.4340.434 0.0980.098 +0.082+0.082 +527.08%+527.08\% ++ CF ⇒ Jaccard 0.3640.364 0.6460.646 0.5160.516 0.1210.121 +0.106+0.106 +674.98%+674.98\% ++ Louvain ⇒ Leiden (Optimal) 0.3640.364 0.6460.646 0.5360.536 0.1260.126 +0.110+0.110 +704.85%+704.85\% KDD TF – CF – Louvain (Baseline) 0.0920.092 0.5000.500 0.2480.248 0.0110.011 - - ++ TF ⇒ LMRank 0.1740.174 0.6010.601 0.4300.430 0.0450.045 +0.033+0.033 +291.46%+291.46\% ++ CF ⇒ Jaccard 0.1740.174 0.6370.637 0.6740.674 0.0750.075 +0.063+0.063 +550.30%+550.30\% ++ Louvain ⇒ Louvain (Optimal) 0.1740.174 0.6370.637 0.6740.674 0.0750.075 +0.063+0.063 +550.30%+550.30\% W TF – CF – Louvain (Baseline) 0.1230.123 0.5000.500 0.1950.195 0.0120.012 - - ++ TF ⇒ KP–Miner 0.1750.175 0.5630.563 0.3790.379 0.0370.037 +0.025+0.025 +209.95%+209.95\% ++ CF ⇒ Cosine 0.1750.175 0.6810.681 0.5710.571 0.0680.068 +0.056+0.056 +464.60%+464.60\% ++ Louvain ⇒ Leiden (Optimal) 0.1750.175 0.6810.681 0.5750.575 0.0680.068 +0.056+0.056 +468.53%+468.53\% SemEval–2017 TF – CF – Louvain (Baseline) 0.2170.217 0.5000.500 0.2110.211 0.0230.023 - - ++ TF ⇒ KeyBERT 0.4850.485 0.5330.533 0.2370.237 0.0610.061 +0.038+0.038 +167.37%+167.37\% ++ CF ⇒ Cosine 0.4850.485 0.6360.636 0.5010.501 0.1540.154 +0.132+0.132 +574.90%+574.90\% ++ Louvain ⇒ Leiden (Optimal) 0.4850.485 0.6360.636 0.5070.507 0.1560.156 +0.134+0.134 +583.33%+583.33\% DUC–2001 TF – CF – Louvain (Baseline) 0.1060.106 0.5000.500 0.2660.266 0.0140.014 - - ++ TF ⇒ LMRank 0.2400.240 0.5750.575 0.3600.360 0.0500.050 +0.035+0.035 +250.52%+250.52\% ++ CF ⇒ Cosine 0.2400.240 0.5580.558 0.6230.623 0.0840.084 +0.069+0.069 +490.39%+490.39\% ++ Louvain ⇒ Louvain (Optimal) 0.2400.240 0.5580.558 0.6230.623 0.0840.084 +0.069+0.069 +490.39%+490.39\% 500N–KP–Crowd TF – CF – Louvain (Baseline) 0.3630.363 0.5000.500 0.1860.186 0.0340.034 - - ++ TF ⇒ TF–IDF 0.3370.337 0.5000.500 0.1530.153 0.0260.026 −0.008-0.008 −24.01%-24.01\% ++ CF ⇒ Cosine 0.3370.337 0.5530.553 0.5700.570 0.1060.106 +0.072+0.072 +213.41%+213.41\% ++ Louvain ⇒ Leiden (Optimal) 0.3370.337 0.5530.553 0.5700.570 0.1060.106 +0.072+0.072 +213.41%+213.41\% Third, as anticipated in Subsection I-D2, even a marginal difference in RI was factored into the results. Substituting CF with Jaccard only increased cs2,x2c_s_2,x_2 from 0.6220.622 to 0.6460.646 for Inspec. Jaccard nonetheless altered the SN topology and edge weight information, thereby influencing the CD stage. Consequently, the relative improvement in J escalated from 527.08%527.08\% to 674.98%674.98\%. Fourth, however, the overall influences of the selected CD algorithms on the relative improvements in J were marginal. When we replaced Louvain with Leiden for NUS, the difference in the approximate J values was negligible. These results were likely attributable to the sparsity of vertex adjacency and edge weight information (Subsubsection I-E2). Future applications leveraging SOTA CD algorithms are expected to enhance SN optimality. Finally, local optimization did not guarantee global optimization. For 500N–KP–Crowd, cs1,x1c_s_1,x_1 of TF was higher than that of TF–IDF. However, J of the optimal process incorporating TF–IDF ultimately exceeded that of the baseline. This result underscores the cascading nature of the SNC stages. V Discussion The previous section has wrapped up the PoC of ClueNetwork by demonstrating that it is a scientifically realistic and practically working framework. The proposed framework and this paper nonetheless come with both contributions and limitations. We now discuss them. Limitations of a framework or paper sometimes suggest potential directions for future work. Hence, certain limitations will be discussed alongside future work. Subsequently, the contributions will be discussed. V-A Limitations and Future Work Extension to Dynamic SNC. Documents are created at different points in time. Although ClueNetwork currently does not account for it, real–time updates of documents can render static SNs outdated. It is necessary to establish an Incremental Document Update Strategy (IDUS), track impacts of dynamic environments on each SNC stage, and compare the performance of SNC policies before and after updates. Nonetheless, we defer ensuring SN timeliness to future work. There are two reasons. First, that extension requires independent work. To compute every document’s impact within a reasonable timeframe, the IDUS should be supported by well–designed data pipelines and algorithms. We have already devoted 3434 pages of this paper solely to ensuring SN optimality. Given the extension’s significance, it would, paradoxically, be an underservice to address the extension within a mere subsection. Second, ClueNetwork can already cover a substantial range of SNs. When we explored multiple articles applying SNC [19], we found that most research teams performed SNC for datasets from narrow time windows. Development of Software Library. ClueNetwork is a framework, yet not a full–fledged software library. Although ClueNetwork in its current state ensures standard reusability required for topical review articles, it does not yet achieve the highest reusability. Developing such a library requires many considerations (the extension to dynamic SNC, coverage of local methods, time and space complexity, among others). Hence, we defer it to future independent work. Inspiration. We humbly acknowledge that ClueNetwork is largely inspired by perspectives of network science established by peers, many of whom are physicists or biologists. For instance, the basic idea that phases or stages of network analysis can be systematically integrated has already been shared by biologists (e.g., [11]) who integrate CD and alignment of protein–protein interaction networks (e.g., [179]–[181]). ClustRNet [141], the origin of Algorithm 1, was also developed by biologists. Percolation theory, on which ClueNetwork heavily relies, has also been established by physicists (e.g., [129], [131]–[134]). V-B Contributions Notwithstanding the limitations, this paper and ClueNetwork contribute to the body of knowledge in the following ways. Revisiting Semantic Networks as Clues. Nowadays, numerous frameworks leveraging KGs for AI–assisted systems (e.g., [182]) are being updated day by day. SNs participate in this trend rarely and thus are placed in a position where they could be misunderstood as inferior approximations of KGs. Accordingly, Subsection I-A has devoted substantial pages to elucidate that SNs can be legitimate symbolic systems representing non–propositional knowledge in terms of abduction. By decoupling SNs and hypotheses derived from them, Subsection I-A has also clarified that SNs cannot be evaluated through fully gold–standard–based approaches. Substantial Methodological Refinement. Against this backdrop, ClueNetwork reformulates the notion of an optimal SN for a textual dataset not as an elusive gold SN, but as some SN that achieves the highest joint confidence for the local objectives (keyness, interpretability, and distinctiveness). Here, while ClueNetwork accepts the existence of gold keyphrases to maintain minimal links with reality, it circumvents elusive gold edge weights (and consequently, elusive gold CD partition). To achieve this circumvention, ClueNetwork incorporates the MCC–based veracity pretest and the percolation–theory–based RI. Although MCC [26] and percolation theory [129] are certainly not our creations, the idea of integrating them into ClueNetwork ultimately facilitates ranking candidate SNs. Therefore, this integration constitutes a substantial methodological refinement of conventional SNC practices. Scientific Transparency. Domain researchers can report their exploratory research by disclosing, “an SN was constructed from the dataset, and its confidence was evaluated at 15.6%15.6\% by using ClueNetwork,” instead of merely stating, “an SN was constructed from the dataset.” That is, ClueNetwork can enhance scientific transparency and provide domain researchers better starting points for their research programs. Composability. Most components (including parameters, local evaluation criteria, and local methods) of ClueNetwork are modular and substitutable. Indeed, we have never argued throughout this paper that they must be exclusively selected. That is, ClueNetwork offers users who want to update SOTA SNC processes opportunities to embed technologically sound components into it. This high composability is an intentional design aimed at sustaining ClueNetwork as a framework for process optimization rather than a singular process. VI Conclusions This paper has reviewed the theoretical foundation of Semantic Networks (SNs) as clues and proposed ClueNetwork that facilitates pinpointing an optimal SN among candidate SNs for a textual dataset. To accomplish both goals, the eight Research Questions (RQs) were formulated in Section I, and this paper has sequentially focused on them. On RQ1 (“How do SNs as clues represent knowledge?”), Subsection I-A has clarified that such SNs represent knowledge by implying data producers’ beliefs as non–propositional triads. The definition of an SN as a clue has also been presented as a system of such triads. On RQ2 (“When are SNs as clues, rather than typical Knowledge Graphs (KGs), recommended to be built?”), Subsection I-A has clarified that while KGs are recommended for works requiring verification–oriented Knowledge Representation (KR), SNs are recommended for works requiring hypothesis–generation–oriented KR. It has also been clarified that, unlike KGs, qualities of SNs are decoupled from the veracity of derived hypotheses concerning what is implied. On RQ3 (“What are the definitions of the SN Construction (SNC) stages and their objectives?”), Subsubsections I-B1–I-D1 have defined Automatic Keyphrase Extraction (AKE), Edge Weighting (EW), and Community Detection (CD) as shown here (link), here (link), and here (link), respectively. Then, Subsubsections I-B1 and I-D1 have defined the objectives of AKE and CD as shown here (link) and here (link), respectively. The objective of EW has also been defined in Subsubsection I-A2 as shown here (link). On RQs 4 (“Which stage–specific methods have been selected for the PoC of ClueNetwork?”) and 6 (“Which stage–specific selected methods yield high performance?”), Subsubsections I-B2–I-D2 have briefed the philosophies of the selected local methods, and Subsubsections I-C2–I-E2 have reported their illustrative evaluation results, respectively. Before that, on RQ5 (“How are the local evaluation criteria defined and justified?”), Subsection I-A has ensured the clear definitions of hF1hF_1 (Table VI), RI ((7)), and Modularity Q ((4)). Their justifications have also been presented as shown here (link), here (link), and here (link). On RQ7 (“How are local evaluation results across the SNC stages integrated to identify the optimal SN?”), Subsection IV-A has first reformulated SNC as a Process Optimization Problem (POP) and presented its objective function J that integrates local evaluation results across AKE, EW, and CD. Then, Subsection IV-B has presented the reusable framework ClueNetwork that incorporates not only J but also the mechanisms of percolation–theory–based evaluation and Matthews–Correlation–Coefficient–(MCC)–based minimal veracity pretest for EW measures. This lightweight framework not only prevents false edges but also facilitates identifying optimal SNs for documents, provided that researchers only prepare much more accessible gold keyphrases without gold edge weights and gold community partitions. On RQ8 (“How is ClueNetwork’s objective function J defined and justified?”), Subsection IV-C has first clarified that J is ultimately the joint subjective probability representing a putative peer reviewer’s belief that keyness, interpretability, and distinctiveness of a given SN have jointly been achieved. Then, the subsection has justified the selected expression of J in two ways. First, it has theoretically explained that the expression aligns with the concept of subjective probability in Bayesian statistics. Second, through the perturbation analysis, the subsection has empirically demonstrated that the expression reacts more strongly against untruth, thereby moving more directly toward truth than the alternatives do. Consequently, by addressing RQs 1 to 4, this paper has confirmed the scientific legitimacy of SNs as clues and reviewed the key concepts and methods associated with the fundamental stages for constructing them. Thereby, their theoretical foundation has been clarified. Furthermore, by addressing RQs 5 to 8, this paper has demonstrated that optimizing SNC is feasible and presented ClueNetwork for it. Appendix A S. Korean One–Way Traffic Sign Non–propositionally structured data can manifest anywhere. For example, the one–way traffic sign in the Republic of Korea (South Korea) is structured as a combination of an up–arrow (↑ ) and the word 일방통행 (one–way): Figure 22: One–way Traffic Sign in S. Korea. This sign is certainly information, yet not a proposition. On public roads, where split–second judgments determine life or death, there is no time to convert the sign into a normative proposition. Nonetheless, the sign can manifest even knowledge, as qualified Korean drivers share a belief that they MUST NOT drive in the opposite direction. In contrast, for those who have not yet embodied the belief, the sign remains some information, yet not knowledge. Some foreigners unfamiliar with Korean have interpreted 일방통행 as 이바토해 2000, as the final consonants ㄹㅇ resemble 2000 to them (link). SNs as clues are also most useful when interpreted by experts who can derive knowledge from such clues. So, Section I states that “the lower bound of the expectation of SNC is the extraction of meaningful information, and the upper bound is knowledge representation.” Appendix B Semantic Relatedness/Similarity Humans can perceive two words as semantically related if there exists at least one semantic or mere lexical relation between them [92, 93]. Such relations are diverse, for instance, antonymy, hypernymy & hyponymy, IS–A, meronymy & holonymy, troponymy, derivation, entailment, and others [95, 96]. Criteria for distinguishing semantic similarity from semantic relatedness are presented in Table XIX. TABLE XIX: Possible Criteria for Determining Whether Similarity beyond Relatedness Exists between Two Words Criterion Description Sharing many properties Whether two words share many properties [91, 92], [96]. Kangaroo and wallaroo are similar because both live in Australia, have pouches, move by hopping, can even attack innocent zoologists, etc. In contrast, kangaroo and Australia are related but not similar. Substitution Whether two words can be substituted for each other “without changing the underlying semantics.” [95] Given that mad can be substituted with crazy, they are similar. While free belongs to the same “semantic field” [94] (i.e., possible mental states of graduate students), it is related to but not similar to the former. Presence of an IS–A relation [92] considers two words similar if a direct or indirect IS–A relation exists between them. Given that pineapple on pizza and Americano coffee can be unforgivable sins to many Italians, they are similar. In such a case, the direct relation between two words does not have to be IS–A. [93] lists possible relations as troponymy, synonymy, hypernymy & hyponymy, or antonymy. Appendix C Why undirected SNs are popular? When a directed edge from “Simpson” to “family” is derived by using CF, it can be inferred that they frequently co–occur as a collocation. However, when the edge is derived by using Cosine, the directional meaning becomes elusive. Moreover, directed edges between multigrams are scarcer than those between unigrams. Furthermore, even if multigrams can be decomposed, it remains unclear how their original scores should be distributed among their constituent unigrams. TABLE X: Overview of Representative Network Types Type Intuition Key Features Base Degree Distribution Base Model Random “The world, ruled by uncertainty…” Low clustering and logarithmic scaling of average path length Single scale (Poisson) Erdős–Rényi [136] Small–world “My friend’s friend is likely my friend!” High clustering and short average path length Single scale (Exponential) Watts–Strogatz [137] Scale–free “The richer get richer.” Dominant hubs and ultra–short average path length Scale–free (Power Law) Barabási–Albert [138] Generalized random “Preserve a given degree distribution, but rewire edges at random.” Preserved degree distribution User–defined Configuration [135] Appendix D Loss of Discriminative Power According to [109], when most entries of vectors are populated wiht meaningless zeros, the zero vector loses its discriminative power; Minkowski then becomes unstable even under small noise; as the dimensionality or the norm parameter p increases, the noise scaling effect is amplified; for a vector, the distance difference between its farthest neighbor and its closest neighbor cannot increase as rapidly as the expected distance between any vector and its closest neighbor; consequently, such differences lose their discriminative power, rendering distances between vectors meaningless and unstable. In contrast, given that Cosine is driven by the dot product of two keyphrases and the discrete measures focus on the set relations between the two, these measures remain free from the problematic |ti,k−tj,k|p|t_i,k-t_j,k|^p. Indeed, for applications such as clustering in high–dimensional sparse spaces, Cosine and Jaccard yield superior performances to even Euclidean [110]. Appendix E Analytical Approximations for fcf_c Tracing back the idea that fcf_c can be purely mathematically derived, there are Molloy and Reed [135] who proved that any random network with ⟨k2⟩/⟨k⟩>2 k^2 / k >2 has a G_GC. Herein, ⟨k⟩ k and ⟨k2⟩ k^2 are the first and second moments of the degree distribution of the G. Cohen et al. [132] derived a closed–form expression for fcf_c from the Molloy–Reed criterion: fcCohen=1−1(⟨k2⟩⟨k⟩−1) f_c^Cohen=1- 1 ( k^2 k -1 ) (13) In fact, numerous networks in the world deviate from purely random networks (Table X), and the Molloy–Reed criterion does not account for triangles in empirical networks. Hence, under the intuition that percolation is hindered as T△T_ increases, Berchenko et al. [139] proposed the heuristic criterion (1−T△)(⟨k2⟩/⟨k⟩−1)>1(1-T_ )( k^2 / k -1)>1 for the existence of G_GC by incorporating the correction term (1−T△)(1-T_ ) into the Molloy–Reed criterion. Thereby, a new closed–form expression for fcf_c [140] was also derived from Berchenko’s heuristic: fcBerchenko=1−1(⟨k2⟩⟨k⟩−1)(1−T△) f_c^Berchenko=1- 1 ( k^2 k -1 )(1-T_ ) (14) In this manner, analytical approximations for fcf_c have progressively incorporated additional properties exhibited by empirical networks. Nevertheless, deriving a universal closed–form expression for fcf_c across diverse networks continues to be an open challenge. Should more comprehensive expressions become available, researchers could estimate fcf_c directly from network statistics without repeated simulations. Appendix F Preprocessing Types Please refer to Table XXI. TABLE XXI: Employed Preprocessing Types Type Description Common Gold keyphrases are tokenized by using spaCy (v3.8.11) [151] with a custom infix finditer. Tokens in each gold keyphrase are stemmed by using the Porter stemmer in NLTK (v3.9.1) [152], and the stems are joined with whitespace. Thereby, stemmed gold keyphrases are obtained. Type 1 Each document is tokenized by using spaCy (v3.8.11) with the infix finditer. Then, 11– to n–grams are identified, and irrelevant n–grams are filtered out by using the candidate_filtering function in PKE [150]. Additional filtering can be applied by certain algorithms. For each n–gram, its surface forms, offsets, and other details are stored in a container by using its lexical form (i.e., the stemmed form produced by the Porter stemmer in NLTK (v3.9.1)) as the key. This key is treated as a candidate, although the stored information may also be referenced by certain algorithms. Type 2 Each document is tokenized and POS–tagged by using spaCy (v3.8.11) with the infix finditer. A graph is then built only based on nouns, proper nouns, and adjectives. Here, PositionRank adopts a stricter filter. Using the RegexParser in NLTK (v3.9.1) with the pattern ¡ADJ¿*¡NOUN—PROPN¿+, PositionRank first identifies NPs. Then, a graph is built for the NPs by using only nouns, proper nouns, and adjectives. Type 3 It is designed for KeyBERT, which cannot obtain appropriate candidates and their contextual embeddings from n–grams or stems. Type 3 exploits a candidate container provided by PKE, as in Types 11 and 22. Here, each document is first tokenized and POS–tagged by using spaCy (v3.8.11) with the infix finditer. Then, among all surface forms of each NP identified by the RegexParser with the pattern, the one with the earliest offset is treated as a candidate. Type 4 Each document is tokenized and POS–tagged by using StanfordCoreNLP (v3.9.1.1) [153]. Next, NP chunking is applied to the tokens by the RegexParser with the pattern ¡N.—J¿¡N.*¿, but any NP containing one or more stopwords from NLTK (v3.9.1), special characters, or punctuation is excluded from candidate consideration. The resulting NPs are then lemmatized by using the WordNetLemmatizer in NLTK (v3.9.1). When multiple lemmas share the same stemmed form, only the one with the highest keyness score is treated as a candidate. Type 5 Each document is tokenized, POS–tagged, and NP–chunked by using spaCy (v3.8.11). Next, phrases that are stopwords, begin with trivial elements (e.g., pronouns, particles, or digits), are shorter than two characters, or contain URL terms or email terms are not regarded as candidates. The optional filters of LMRank can also be used. When multiple NPs share the same stemmed form, only the one with the highest keyness score is treated as a candidate. Appendix G About Normality Test When observations are sparse, and when all observations are zero (in which case SciPy [98] mechanically judges there is no evidence against normality), the K–S test [155] and the S–W test [160] are prone to Type I errors, respectively. When magnitudes of observations are extremely small, variance compression also misleads the S–W test to Type I errors. Acknowledgment Please refer to the following items. 1. This research was supported by the G-LAMP Program of the National Research Foundation of Korea (NRF) grant funded by the Ministry of Education (No. RS-2025-25441317). 2. The regression analysis class taught by Prof. ChanWoo Yoo, working in the Division of Advanced Engineering, Korea National Open University, enhanced the first author’s statistical foundation. 3. Yongjae Oh, a Ph.D. candidate in the Department of Physics and Astronomy, Seoul National University, provided insightful advice on percolation theory. 4. We express our gratitude to the reviewers for thoroughly reading this lengthy (yet inevitably so) paper. 5. Several figures in this paper were created using Gemini 3.5 Flash [41] or purchased with commercial licenses. Specifically, Fig. 3 as a whole, the Einstein icon in Fig. 2, and the diamond icon in Fig. 19 were generated by Gemini 3.5 Flash [41]. Most of the remaining icons in Fig. 19 were commercially acquired. 6. Except for the mentioned figures, we have created all content related to this work. 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Acids Res., vol. 49, no. D1, p. D605–D612, Jan. 2021. Accessed on: Mar. 8, 2026, DOI:10.1093/nar/gkaa1074 [182] D. Edge et al., “From Local to Global: A GraphRAG Approach to Query-Focused Summarization,” unpublished, 2024. [Online]. Available: 10.48550/arXiv.2404.16130. Accessed on: Sep. 9, 2025. [183] Anthrophic, System Card: Claude Sonnet 4.6, Feb. 2026. [Online]. Available:shortened link. Accessed on: Aug. 2, 2026. [184] A. Singh et al., “OpenAI GPT-5 System Card,” unpublished, 2025. [Online]. Available: 10.48550/arXiv.2601.03267. Accessed on: Aug. 2, 2026. JINWOO HA will join the Department of Industrial and Information Systems Engineering at Soongsil University, Seoul, Republic of Korea, in September 2026 as an incoming Ph.D. student. He will receive the B.Eng. degree in AI from Korea National Open University in August 2026. Previously, he received the B.A. degree in philosophy with cum laude distinction from Chung–Ang University, Seoul, Republic of Korea, in 2020, and the M.S. degree in IT distribution and logistics from Soongsil University in 2024. His research interests include network science, knowledge engineering, process science, AI, and philosophy of AI. DONGSOO KIM received the B.S., M.S., and Ph.D. degrees in industrial engineering from Seoul National University, Seoul, Republic of Korea, in 1994, 1996, and 2001. From 2003 to 2005 and 2005 to 2006, he was an Instructor and then an Assistant Professor at the Graduate School of Healthcare Management and Policy at The Catholic University of Korea. From 2006 to 2009 and from 2009 to 2015, he was an Assistant Professor, and Associate Professor at the Department of Industrial and Information Systems Engineering, Soongsil University, Seoul, Republic of Korea. Since 2015, he has been a Full Professor at the Department of Industrial and Information Systems Engineering, Soongsil University. He serves as an Associate Editor of the ICIC Express Letters journal and the Dean of the College of Engineering at Soongsil University. His research interests include business process management, process mining for process optimization, industrial intelligent systems, medical informatics and u–health, convergence technologies of logistics, distribution, and information, and information security management systems. Prof. Dongsoo Kim was a recipient of the International Conference on Innovative Computing, Information, and Control Contribution Award in 2015 and the International Symposium on Information and Knowledge Management Best Poster Award in 2020.

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