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STAG-CN: Spatio-Temporal Apiary Graph Convolutional Network for Disease Onset Prediction in Beehive Sensor Networks

Sungwoo Kang

Year: 2026Venue: arXiv preprintArea: cs.LGType: PreprintEmbeddings: 52

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Summary

The paper introduces the Spatio-Temporal Apiary Graph Convolutional Network (STAG-CN), a graph neural network designed for disease onset prediction in beehive sensor networks. By modeling inter-hive relationships through a dual adjacency graph (physical co-location and climatic sensor correlation) and utilizing a temporal-spatial-temporal sandwich architecture, the model captures disease-relevant contagion dynamics. Evaluation on the Korean AI Hub apiculture dataset demonstrates that climatic correlations provide stronger predictive signals for disease onset than physical proximity alone.

Entities (4)

Korean AI Hub apiculture dataset · dataset · 100%STAG-CN · model · 100%Chebyshev spectral graph convolution · method · 95%Precision Apiculture · domain · 90%

Relation Signals (3)

STAG-CN → evaluatedon → Korean AI Hub apiculture dataset

confidence 100% · Evaluated on the Korean AI Hub apiculture dataset (dataset #71488)

STAG-CN → usesarchitecture → temporal-spatial-temporal sandwich

confidence 95% · processes multivariate IoT sensor streams through a temporal--spatial--temporal sandwich architecture

Climatic adjacency matrix → predicts → disease onset

confidence 90% · climatic adjacency matrix alone matches full-model performance

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Abstract

Abstract:Honey bee colony losses threaten global pollination services, yet current monitoring systems treat each hive as an isolated unit, ignoring the spatial pathways through which diseases spread across apiaries. This paper introduces the Spatio-Temporal Apiary Graph Convolutional Network (STAG-CN), a graph neural network that models inter-hive relationships for disease onset prediction. STAG-CN operates on a dual adjacency graph combining physical co-location and climatic sensor correlation among hive sessions, and processes multivariate IoT sensor streams through a temporal--spatial--temporal sandwich architecture built on causal dilated convolutions and Chebyshev spectral graph convolutions. Evaluated on the Korean AI Hub apiculture dataset (dataset \#71488) with expanding-window temporal cross-validation, STAG-CN achieves an F1 score of 0.607 at a three-day forecast horizon. An ablation study reveals that the climatic adjacency matrix alone matches full-model performance (F1\,=\,0.607), while the physical adjacency alone yields F1\,=\,0.274, indicating that shared environmental response patterns carry stronger predictive signal than spatial proximity for disease onset. These results establish a proof-of-concept for graph-based biosecurity monitoring in precision apiculture, demonstrating that inter-hive sensor correlations encode disease-relevant information invisible to single-hive approaches.

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STAG-CN: Spatio-Temporal Apiary Graph Convolutional Network for Disease Onset Prediction in Beehive Sensor Networks Sungwoo Kang Abstract Honey bee colony losses threaten global pollination services, yet current monitoring systems treat each hive as an isolated unit, ignoring the spatial pathways through which diseases spread across apiaries. This paper introduces the Spatio-Temporal Apiary Graph Convolutional Network (STAG-CN), a graph neural network that models inter-hive relationships for disease onset prediction. STAG-CN operates on a dual adjacency graph combining physical co-location and climatic sensor correlation among hive sessions, and processes multivariate IoT sensor streams through a temporal–spatial–temporal sandwich architecture built on causal dilated convolutions and Chebyshev spectral graph convolutions. Evaluated on the Korean AI Hub apiculture dataset (dataset #71488) with expanding-window temporal cross-validation, STAG-CN achieves an F1 score of 0.607 at a three-day forecast horizon. An ablation study reveals that the climatic adjacency matrix alone matches full-model performance (F1 = 0.607), while the physical adjacency alone yields F1 = 0.274, indicating that shared environmental response patterns carry stronger predictive signal than spatial proximity for disease onset. These results establish a proof-of-concept for graph-based biosecurity monitoring in precision apiculture, demonstrating that inter-hive sensor correlations encode disease-relevant information invisible to single-hive approaches. I Introduction Managed honey bee colonies are indispensable to global agriculture, underpinning the pollination of roughly one-third of food crops [1, 2]. Over the past two decades, however, beekeepers worldwide have reported unsustainable annual colony losses driven by pathogens, parasites, pesticide exposure, and habitat degradation [3, 4]. These losses motivate the development of automated, sensor-driven monitoring systems that can detect health anomalies before colonies collapse. Precision apiculture has made considerable progress in instrumenting individual hives with temperature, humidity, weight, acoustic, and gas sensors [5, 6, 7]. Machine learning models trained on these streams have demonstrated success in detecting queen loss [8], swarming events [9], and abnormal brood temperature profiles [10]. Nevertheless, these approaches share a common limitation: they treat each hive as a statistically independent unit, learning per-hive classifiers without regard for the spatial and environmental relationships among hives within an apiary. This isolation assumption is problematic because many honey bee diseases—including American foulbrood, European foulbrood, and Nosema infections—propagate between hives through drifting and robbing bees, shared foraging resources, and beekeeper management practices [12, 13]. An outbreak in one hive elevates the risk for its neighbors, creating spatio-temporal contagion dynamics that purely per-hive models cannot capture. The epidemiological literature on livestock and wildlife disease has long recognized network structure as a first-class predictor of outbreak spread [14, 15], yet no prior work has applied graph-based modeling to inter-hive disease prediction in apiculture. Spatio-temporal graph convolutional networks (STGCNs) offer a natural framework for this problem. Originally developed for traffic flow forecasting [18, 19], STGCNs jointly model temporal dynamics and spatial dependencies on graph-structured data. Their success in domains where sensor nodes share implicit or explicit relationships—traffic intersections, air quality stations, power grid nodes [20, 21]—suggests applicability to apiary sensor networks, where hive sessions are nodes connected by physical proximity and shared environmental conditions. This paper proposes the Spatio-Temporal Apiary Graph Convolutional Network (STAG-CN), which adapts the STGCN paradigm to disease onset prediction in beehive sensor networks. STAG-CN constructs a dual adjacency graph encoding both physical co-location and pairwise climatic sensor correlation, then processes multivariate sensor time series through a sandwich architecture of causal temporal convolutions and Chebyshev spectral graph convolutions. The contributions of this work are as follows: 1. We formulate apiary disease prediction as a node-level binary classification task on a spatio-temporal graph, providing the first graph-based disease model for precision apiculture. 2. We propose a dual adjacency construction that combines physical topology with climatic sensor correlation, enabling the graph to capture both explicit spatial proximity and implicit environmental similarity. 3. We demonstrate that the climatic adjacency component alone accounts for the full predictive performance of STAG-CN (F1 = 0.607), while the physical adjacency alone yields substantially lower performance (F1 = 0.274), revealing that shared environmental response patterns carry stronger disease-predictive signal than physical co-location. 4. We establish honest evaluation baselines using expanding-window temporal cross-validation and leave-one-group-out protocols, reporting both strengths and limitations of the approach on a small, real-world dataset. The remainder of this paper is organized as follows. Section I reviews related work in hive health monitoring, spatio-temporal graph networks, and disease spread modeling. Section I describes the Korean AI Hub apiculture dataset. Section IV presents the STAG-CN methodology. Section V details the experimental setup. Section VI reports results and ablation studies. Section VII discusses implications and limitations. Section VIII concludes. I Related Work I-A Sensor-Based Hive Health Monitoring The use of IoT sensors for hive monitoring dates to early weight-based studies by Meikle et al. [5], who showed that continuous weight measurement can track nectar flow and colony growth. Subsequent work expanded the sensor palette to include temperature [10], humidity [6], sound [8, 9], and gas concentrations [11]. Zacepins et al. [7] surveyed the field and identified key challenges including sensor drift, missing data, and the difficulty of obtaining ground-truth disease labels. Machine learning classifiers applied to these streams—random forests, SVMs, and recurrent networks—have achieved promising per-hive accuracy for specific conditions such as queenlessness and swarming, but none model inter-hive dependencies. STAG-CN addresses this gap by treating hive sessions as nodes in a graph and learning from the collective sensor signal across the apiary. I-B Spatio-Temporal Graph Neural Networks Graph neural networks (GNNs) extend deep learning to non-Euclidean data [16, 17]. For time series on graphs, Yu et al. [18] proposed STGCN, which alternates temporal convolutions with Chebyshev spectral graph convolutions to capture both temporal and spatial dependencies. Li et al. [19] introduced DCRNN using diffusion convolutions and a recurrent encoder that replaces standard GRU matrix multiplies with graph diffusion operations. Wu et al. [20] proposed Graph WaveNet, which combines adaptive adjacency learning—via learnable node embeddings—with dilated causal convolutions and diffusion-based spatial aggregation. Both DCRNN and Graph WaveNet are included as baselines in our evaluation (Section V-B) to provide a stronger comparison against established spatio-temporal graph models. These architectures were designed for traffic forecasting on large urban networks with thousands of nodes. Their application to biological sensor networks remains unexplored. STAG-CN adapts the temporal–spatial–temporal sandwich architecture of [18] to a small, sparse apiary graph, introducing a dual adjacency construction motivated by the distinct roles of physical proximity and environmental similarity in disease transmission. I-C Disease Spread as Network Contagion Epidemiological modeling has long used network structure to predict disease propagation. Keeling and Eames [14] demonstrated that contact network topology governs outbreak size and speed in livestock populations. Craft [15] extended this framework to wildlife, showing that even coarse network proxies—spatial proximity, shared habitat—improve transmission predictions beyond homogeneous mixing models. In apiculture, Fries and Camazine [12] and Peck and Seeley [13] documented inter-colony transmission pathways for Varroa mites and bacterial brood diseases, but this biological evidence has not been translated into computational graph models. STAG-CN bridges this gap by encoding known transmission-relevant structure—physical co-location and environmental correlation—into a learnable adjacency matrix for disease prediction. I Dataset I-A Korean AI Hub Apiculture Dataset The data originate from the Korean AI Hub intelligent apiculture dataset (dataset #71488), which provides IoT sensor recordings and annotated inspection labels from managed apiaries. The dataset spans six apiary groups, each containing multiple hive sessions instrumented with multimodal sensors. Sensor data and disease labels are provided in separate directories (XLSX files for sensors, JSON files for annotations), with an overlapping temporal window from 14 July 2022 to 30 September 2022 (79 calendar days) during which both modalities are concurrently available. I-B Sensor Features Each hive session records eight sensor channels: temperature, humidity, weight, tilt, methane, ammonia, carbon monoxide, and sound. Raw readings arrive at sub-daily intervals. The preprocessing pipeline aggregates readings to daily resolution using four summary statistics per channel (mean, standard deviation, minimum, maximum), yielding F=8×4=32F=8× 4=32 features per node per day. Missing values are forward-filled then backward-filled within each group. All features undergo global z-score normalization across groups, ensuring zero mean and unit variance for each of the 32 dimensions. I-C Disease Label Extraction Disease annotations are embedded in JSON filenames following a structured naming convention: group_sub_cond_…_date_session_seq.json, where the condition field takes value D (disease) or R (healthy). Labels are aggregated per (group, session, date) triplet by computing a severity index: the ratio of disease-flagged files to total files. A binary label is assigned as positive (y=1y=1) if any disease annotation exists for that triplet. This extraction procedure yields sparse, temporally irregular labels—not every node has a label on every day—necessitating a mask mechanism during training and evaluation. Table I summarizes the dataset statistics. Disease labels are concentrated in group 01_1, which is the only group exhibiting disease onset within the overlap period. This concentration has important consequences for cross-validation design, as discussed in Section V. TABLE I: Dataset statistics. The overlap window spans 79 calendar days during which both sensor and label data are available. Disease labels are concentrated in a single apiary group (01_1), yielding 27 positive labels out of 473 total annotations across 49 hive-session nodes. Statistic Value Apiary groups 6 Hive-session nodes (N) 49 Overlap window (days) 79 Total label annotations 473 Disease-positive labels 27 (5.71%) Valid sliding-window samples 44 Sensor channels 8 Features per node per day (F) 32 DateJul 14Aug 15Sep 30S01S02S03S04S05DiseaseHealthyGroup 01_1 Figure 1: Schematic disease timeline for group 01_1, the only apiary group exhibiting disease onset during the overlap period. Filled circles indicate disease-positive labels; open circles indicate healthy labels. Disease appears in late August and spreads across sessions in a staggered pattern, consistent with inter-hive contagion dynamics. IV Methodology IV-A Problem Formulation Consider an apiary sensor network represented as a graph =(,ℰ)G=(V,E), where V is a set of N hive-session nodes and ℰE encodes pairwise relationships. At each discrete time step t, node i produces a feature vector i(t)∈ℝFx_i^(t) ^F comprising F=32F=32 daily sensor statistics. Given a lookback window of W days, the input tensor is (t)∈ℝN×W×FX^(t) ^N× W× F, containing the sensor readings for all nodes over the interval [t−W,t)[t-W,t). The task is binary node-level classification: for each node i, predict the disease label yi(t+δ)∈0,1y_i^(t+δ)∈\0,1\ at a future time step t+δt+δ, where δ is the forecast horizon. Not all nodes have labels at every time step; a binary mask mi(t+δ)∈0,1m_i^(t+δ)∈\0,1\ indicates label availability, and only masked-in predictions contribute to the loss and evaluation metrics. IV-B Graph Construction The adjacency matrix encodes prior knowledge about inter-hive relationships. Two complementary matrices capture different aspects of these relationships. The physical adjacency matrix phys∈ℝN×NA_phys ^N× N encodes spatial co-location. Entry (phys)ij=1(A_phys)_ij=1 if nodes i and j belong to the same apiary group, and (phys)ij=0(A_phys)_ij=0 otherwise. This matrix captures the intuition that hives within the same apiary share exposure to drifting bees, robbing events, and beekeeper interventions. The climatic adjacency matrix clim∈ℝN×NA_clim ^N× N encodes environmental similarity. For each pair of apiary groups, the mean Pearson correlation coefficient is computed across all eight base sensor channels (using the mean aggregation) over their shared date range: ρgi,gj=1||∑c∈corr(gi(c),gj(c)), _g_i,g_j= 1|C| _c corr\! (s_g_i^(c),\,s_g_j^(c) ), (1) where C is the set of sensor channels, and g(c)s_g^(c) is the daily mean time series for channel c in group g. Correlations below a threshold τ=0.3τ=0.3 are set to zero. Node-level entries inherit the group-level correlation: (clim)ij=ρgi,gj(A_clim)_ij= _g_i,g_j if ρgi,gj≥τ _g_i,g_j≥τ, and zero otherwise. The combined adjacency matrix blends both components through a mixing parameter λ∈[0,1]λ∈[0,1]: =λphys+(1−λ)clim.A=λ\,A_phys+(1-λ)\,A_clim. (2) Self-loops are added (ii←ii+1A_i _i+1), and the result is symmetrically normalized: ~=−1/2−1/2, A=D^-1/2\,A\,D^-1/2, (3) where D is the degree matrix with Dii=∑jAijD_i= _jA_ij. The normalized matrix ~ A is converted to sparse COO format (edge index and edge weights) for use with the graph convolution layers. Figure 2 illustrates the construction pipeline. physA_physBinaryco-locationclimA_climPearsoncorrelation=λphys+(1−λ)climA= _phys+(1-λ)A_clim~=−1/2−1/2 A=D^-1/2AD^-1/2λ 1−λ1-λ Figure 2: Dual adjacency graph construction. The physical adjacency physA_phys captures binary co-location within apiary groups. The climatic adjacency climA_clim captures pairwise Pearson correlation of sensor time series across groups. The combined matrix A is a weighted blend controlled by λ, followed by self-loop addition and symmetric normalization to produce ~ A. IV-C Temporal Convolutional Block Temporal dependencies within each node’s sensor stream are captured by a causal dilated convolutional network. Each temporal block applies two parallel causal convolutions with a gated activation mechanism: =tanh⁡(f∗d)⊙σ(g∗d),h= \! (W_f*_dx ) σ\! (W_g*_dx ), (4) where ∈ℝCin×Tx ^C_in× T is the input sequence for a single node, fW_f and gW_g are the filter and gate convolution kernels respectively, ∗d*_d denotes causal convolution with dilation factor d, ⊙ is element-wise multiplication, and σ(⋅)σ(·) is the sigmoid function. The gating mechanism allows the network to control information flow, suppressing irrelevant temporal features while amplifying disease-predictive patterns. Each temporal block includes a residual connection and batch normalization: =BN(+r),y=BN\! (h+W_rx ), (5) where rW_r is a 1×11× 1 convolution that projects x to match the output dimension when Cin≠CoutC_in≠ C_out, and BN(⋅)BN(·) denotes batch normalization. A stack of two temporal blocks with dilation factors d∈1,2d∈\1,2\ forms one TCN stack, providing a receptive field that grows exponentially with depth while maintaining causal ordering. IV-D Spatial Convolutional Block Spatial dependencies across nodes are modeled using Chebyshev spectral graph convolutions [17]. The Chebyshev convolution of order K approximates the spectral graph convolution as a K-th order polynomial of the normalized graph Laplacian: =∑k=0K−1Tk(~)k,Z= _k=0^K-1T_k( L)\,X\, _k, (6) where ∈ℝN×CinX ^N× C_in is the node feature matrix, ~=2/λmax− L=2L/ _ -I is the scaled Laplacian, Tk(⋅)T_k(·) is the k-th Chebyshev polynomial, k∈ℝCin×Cout _k ^C_in× C_out are learnable parameters, and ∈ℝN×CoutZ ^N× C_out is the output. The Chebyshev order K=3K=3 allows each node to aggregate information from neighbors up to three hops away. The spatial block applies batch normalization, ReLU activation, and dropout after the Chebyshev convolution. IV-E ST-Block Architecture The core building block of STAG-CN is the ST-Block, which follows a temporal–spatial–temporal sandwich structure [18]: (l)=LN(TCN2(GCN(TCN1((l−1))))+res(l−1)),H^(l)=LN (TCN_2\! (GCN\! (TCN_1\! (H^(l-1) ) ) )\\ +W_res\,H^(l-1) ), (7) where (l−1)∈ℝB×N×T×CH^(l-1) ^B× N× T× C is the input to the l-th block, TCN1TCN_1 and TCN2TCN_2 are TCN stacks (Section IV-C), GCNGCN is the Chebyshev spatial block (Section IV-D), resW_res is the residual projection, and LN(⋅)LN(·) denotes layer normalization. The first temporal block captures local temporal patterns, the spatial block propagates information across the graph, and the second temporal block integrates the spatially enriched features back into the temporal sequence. The full STAG-CN architecture, illustrated in Fig. 3, stacks L=2L=2 ST-Blocks preceded by a linear input projection (F→ChF→ C_h) and followed by a temporal output convolution (taking the last time step) and a two-layer classifier with ReLU activation and dropout: y^i=σ(2⊤ReLU(1i(L)[−1]+1)+b2), y_i=σ\! (w_2 \,ReLU\! (W_1\,h_i^(L)[-1]+b_1 )+b_2 ), (8) where i(L)[−1]∈ℝChh_i^(L)[-1] ^C_h is the hidden representation of node i at the final time step after L ST-Blocks, 1∈ℝ(Ch/2)×ChW_1 ^(C_h/2)× C_h and 2∈ℝCh/2w_2 ^C_h/2 are classifier weights, and σ(⋅)σ(·) is the sigmoid function producing the disease probability y^i∈[0,1] y_i∈[0,1]. ST-Block ×2× 2Input∈ℝB×N×T×FX ^B× N× T× FLinear ProjectionF→ChF→ C_hTCN Stack 1ChebConv (K=3K=3)TCN Stack 2+ Residual + LayerNormTemporal Pooling(last step)ClassifierCh→Ch/2→1C_h→ C_h/2→ 1^∈ℝB×N y ^B× N~ AEdge index+ weights Figure 3: STAG-CN architecture. The input tensor passes through a linear projection, two stacked ST-Blocks (each containing a TCN–GCN–TCN sandwich with residual connections and layer normalization), temporal pooling at the last time step, and a two-layer classifier producing per-node disease probabilities. The normalized adjacency ~ A is shared across all spatial convolution layers. IV-F Loss Function Disease labels constitute 5.71% of all annotations, creating severe class imbalance. Focal loss [22] addresses this by down-weighting well-classified examples and focusing learning on hard cases: ℒFL=−1|ℳ|∑(i,t)∈ℳαt(1−pt)γlog⁡(pt),L_FL=- 1|M| _(i,t) _t\,(1-p_t)^γ\, (p_t), (9) where ℳM is the set of valid (masked-in) node-time pairs, pt=y^ip_t= y_i if yi=1y_i=1 and pt=1−y^ip_t=1- y_i if yi=0y_i=0, αt _t is a class-balancing weight (α=0.75α=0.75 for the positive class, 1−α=0.251-α=0.25 for the negative class), and γ=2.0γ=2.0 is the focusing parameter. The label mask mi(t)∈0,1m_i^(t)∈\0,1\ ensures that only nodes with available annotations contribute to the loss, preventing the model from being penalized on unlabeled node-time pairs. IV-G Adaptive Graph Learning The predefined adjacency matrices physA_phys and climA_clim encode prior knowledge, but the true disease transmission topology may differ from these hand-crafted relationships. We investigate two adaptive adjacency learning mechanisms that allow the model to discover graph structure from data. Node Embedding Adjacency Two learnable embedding matrices 1,2∈ℝN×deE_1,E_2 ^N× d_e generate a static adaptive adjacency: adp=softmax(ReLU(12⊤)),A_adp=softmax\! (ReLU(E_1\,E_2 ) ), (10) where softmax is applied row-wise. This adjacency is learned during training but does not depend on input features. Attention Adjacency A GAT-like attention mechanism [16] produces a dynamic, input-dependent adjacency: αij=exp⁡(LeakyReLU(⊤[i∥j]))∑kexp⁡(LeakyReLU(⊤[i∥k])), _ij= \! (LeakyReLU(a [Wh_i\|Wh_j]) ) _k \! (LeakyReLU(a [Wh_i\|Wh_k]) ), (11) where ∈ℝda×FW ^d_a× F is a shared linear projection, ∈ℝ2daa ^2d_a is the attention vector, and ∥\| denotes concatenation. In both cases, the adaptive adjacency is combined with the predefined adjacency: combined=~+adpA_combined= A+A_adp, followed by renormalization. This allows the model to augment the hand-crafted graph with learned relationships while preserving the prior structure. IV-H Multimodal Feature Integration The Korean AI Hub dataset includes image-based inspection annotations in addition to IoT sensor streams. Rather than requiring a CNN for image processing, we extract 16 annotation-derived features from the JSON label files: (1) total image count per node-day, (2) disease-condition ratio, (3–7) lifecycle stage distribution (5 categories), (8–12) species distribution (5 categories), (13) mean annotations per image, (14–15) bounding box area mean and standard deviation, and (16) raw disease image count. All features are z-score normalized. These image-derived features are integrated via early fusion: they are concatenated with the sensor features along the feature dimension, producing an extended input (t)∈ℝN×W×(F+Fimg)X^(t) ^N× W×(F+F_img) where Fimg=16F_img=16. This approach requires no architectural changes to STAG-CN beyond adjusting the input projection dimension from F=32F=32 to F+Fimg=48F+F_img=48. Table I summarizes the notation used throughout this paper. Table I lists the model hyperparameters and architectural details. TABLE I: Notation summary. All symbols are defined at their first use in the text and collected here for reference. Symbol Definition =(,ℰ)G=(V,E) Apiary sensor graph (nodes, edges) N Number of hive-session nodes F Feature dimension per node per day (32) W Lookback window size in days δ Forecast horizon in days (t)∈ℝN×W×FX^(t) ^N× W× F Input sensor tensor at time t yi(t)∈0,1y_i^(t)∈\0,1\ Disease label for node i at time t mi(t)∈0,1m_i^(t)∈\0,1\ Label availability mask physA_phys Physical adjacency (binary co-location) climA_clim Climatic adjacency (Pearson correlation) λ Adjacency mixing parameter ~ A Symmetrically normalized adjacency K Chebyshev polynomial order Tk(⋅)T_k(·) k-th Chebyshev polynomial ChC_h Hidden dimension L Number of ST-Blocks α,γα,γ Focal loss parameters TABLE I: Model hyperparameters and architectural details for STAG-CN. The total parameter count of 232,257 reflects the input projection, two ST-Blocks, temporal output convolution, and two-layer classifier. Category Parameter Value Architecture Input features (F) 32 Hidden dimension (ChC_h) 64 ST-Blocks (L) 2 TCN kernel size 3 Chebyshev order (K) 3 Training Lookback window (W) 7 days Forecast horizon (δ) 3 days Batch size 16 Learning rate 0.001 Weight decay 10−410^-4 Dropout 0.3 Optimization Max epochs 200 Early stopping patience 15 LR scheduler ReduceOnPlateau Gradient clipping 5.0 Focal loss α (positive weight) 0.75 γ (focusing) 2.0 Graph λ (adjacency mix) 0.5 Correlation threshold (τ) 0.3 Total parameters 232,257 V Experimental Setup V-A Evaluation Protocol Two cross-validation strategies evaluate STAG-CN under complementary assumptions. The primary strategy is expanding-window temporal cross-validation with three folds. Fold k trains on the first (k+1)/(nfolds+1)(k+1)/(n_folds+1) fraction of the chronologically ordered samples and tests on the subsequent 1/(nfolds+1)1/(n_folds+1) fraction. This ensures strict temporal ordering: the model always trains on past data and predicts future disease events, preventing look-ahead bias. Figure 4 illustrates the splitting scheme. The secondary strategy is leave-one-group-out (LOGO) cross-validation with node-level masking. All 44 samples are used in every fold; the held-out group’s nodes are masked during training and unmasked during evaluation. This tests the model’s ability to generalize to unseen hive locations. Because disease labels exist only in group 01_1, only one of six folds produces a meaningful test evaluation. This honest limitation is reported rather than obscured. Fold 1Fold 2Fold 3TimeTrainTest Figure 4: Expanding-window temporal cross-validation with three folds. Each fold trains on all data preceding the test window, ensuring that the model never observes future samples during training. The training set grows with each fold while the test window remains fixed in size. V-B Baselines Five baselines isolate the contributions of graph structure, temporal modeling, and adaptive graph learning. The threshold baseline applies a rule-based classifier that predicts disease when the mean temperature and mean humidity over the lookback window exceed optimized thresholds. The thresholds are determined by grid search on the training set, maximizing F1 score. This baseline tests whether simple environmental thresholds suffice for disease prediction. The LSTM baseline replaces STAG-CN with a two-layer LSTM operating independently on each node’s sensor time series, followed by the same two-layer classifier. This baseline captures temporal dynamics but ignores inter-hive graph structure, isolating the contribution of spatial modeling. The GCN-only baseline uses two stacked Chebyshev graph convolution layers operating on only the last time step’s features (no temporal history), followed by the same classifier. This baseline captures spatial relationships but ignores temporal evolution, isolating the contribution of temporal modeling. The Graph WaveNet [20] baseline combines adaptive adjacency learning (learnable node embeddings 1,2∈ℝN×10E_1,E_2 ^N× 10), K=2K=2 step diffusion convolution (forward and backward random walks plus the adaptive matrix), and gated dilated causal convolutions. We use a lightweight configuration (Ch=32C_h=32, 2 layers, dilation 1,2\1,2\) appropriate for the small graph. The DCRNN [19] baseline replaces GRU matrix multiplies with K=2K=2 step diffusion convolution, processing the temporal sequence step-by-step and using the final hidden state for classification. We use one GRU layer with Ch=32C_h=32. V-C Threshold Calibration Protocol The default classification threshold of 0.5 may not be optimal, particularly for the LOGO setting where the model must generalize to unseen apiaries. We implement a chronological threshold calibration protocol: the first 30% of held-out predictions (ordered by time) form a calibration set on which the threshold maximizing F1 is selected via a sweep from 0.05 to 0.95; the remaining 70% form the evaluation set on which final metrics are computed at the calibrated threshold. We also report the globally optimal threshold (found on the full held-out set) as an upper bound. V-D Metrics F1 score is the primary metric, as it balances precision and recall under class imbalance. Precision, recall, and area under the receiver operating characteristic curve (AUROC) are reported as secondary metrics. All metrics are computed on valid (masked) predictions only, using a classification threshold of 0.5 on the sigmoid output. Cross-validation results report the mean and standard deviation across folds. VI Results VI-A Temporal Cross-Validation Table IV presents the primary temporal cross-validation results across six models. STAG-CN and the GCN-only baseline both achieve F1 = 0.607, outperforming all baselines. Graph WaveNet and DCRNN both achieve F1 = 0.274, substantially below STAG-CN despite incorporating graph-based diffusion convolutions. The threshold baseline achieves F1 = 0.418, while the LSTM fails entirely with zero F1. The shared performance of STAG-CN and GCN-only suggests that for this dataset, spatial information from the graph convolution is the primary driver of disease prediction, while the additional temporal modeling in STAG-CN does not provide incremental benefit. This result is consistent with the small temporal window (7 days) and limited sample size (44 samples), which may not provide sufficient temporal variation for the TCN layers to exploit beyond what a single-day snapshot captures. The threshold baseline achieves F1 = 0.418 with recall matching STAG-CN (0.667), indicating that environmental thresholds capture some disease-relevant signal but produce more false positives (precision = 0.325 vs. 0.565). The complete failure of the LSTM (AUROC = 0.042) confirms that per-node temporal modeling without graph structure is insufficient in this sparse-label, multi-site regime. Graph WaveNet and DCRNN, despite incorporating diffusion-based graph convolutions, underperform even the threshold baseline (F1 = 0.274 vs. 0.418). Their low AUROC values (0.106 and 0.146) suggest that the diffusion-based spatial processing and adaptive adjacency learning in these architectures overfit on this small dataset, where Chebyshev spectral convolutions with a predefined adjacency provide more stable performance. TABLE IV: Temporal cross-validation results (3 folds, expanding window). F1 is the primary metric. STAG-CN and GCN-only achieve the highest F1, outperforming all baselines including the stronger Graph WaveNet and DCRNN models. Values are mean ± standard deviation. Model F1 Precision Recall AUROC STAG-CN 0.607± 0.435 0.565± 0.419 0.667± 0.471 0.563± 0.418 GCN-only 0.607± 0.435 0.565± 0.419 0.667± 0.471 0.583± 0.425 Graph WaveNet 0.274± 0.387 0.232± 0.328 0.333± 0.471 0.106± 0.149 DCRNN 0.274± 0.387 0.232± 0.328 0.333± 0.471 0.146± 0.206 Threshold 0.418± 0.335 0.325± 0.286 0.667± 0.471 N/A LSTM 0.000± 0.000 0.000± 0.000 0.000± 0.000 0.042± 0.059 VI-B Ablation: Adjacency Components Table V isolates the contributions of the two adjacency components. The climatic adjacency alone (λ=0λ=0) achieves the same F1 as the full model (λ=0.5λ=0.5), while the physical adjacency alone (λ=1λ=1) yields a substantially lower F1 of 0.274. This result indicates that environmental sensor correlation, rather than spatial co-location, drives STAG-CN’s disease predictions. The dominance of climatic adjacency aligns with the dataset’s structure: disease is concentrated in a single group (01_1), so the physical adjacency connects diseased nodes primarily to other diseased nodes within the same group. The climatic adjacency, by contrast, connects groups based on shared environmental response patterns, potentially providing a more informative signal about the conditions under which disease emerges. TABLE V: Ablation study on adjacency matrix components (temporal CV, 3 folds). λ=1λ=1: physical adjacency only. λ=0λ=0: climatic adjacency only. λ=0.5λ=0.5: combined (default). The climatic adjacency alone matches the full model, while physical adjacency alone yields substantially lower performance. Configuration F1 AUROC physA_phys only (λ=1λ=1) 0.274± 0.387 0.202± 0.286 climA_clim only (λ=0λ=0) 0.607± 0.435 0.563± 0.418 Combined (λ=0.5λ=0.5) 0.607± 0.435 0.563± 0.418 VI-C Adaptive Graph Learning Table VI presents the ablation results for adaptive graph learning. Both the node embedding and attention-based adaptive adjacency mechanisms are evaluated in combination with the predefined dual adjacency. TABLE VI: Adaptive graph learning ablation (temporal CV, 3 folds). STAG-CN with adaptive adjacency modules compared to the base model with predefined adjacency only. Both adaptive variants match base F1 but differ in AUROC. Configuration F1 AUROC STAG-CN (predefined) 0.607± 0.435 0.563± 0.418 + Embedding adaptive 0.607± 0.435 0.527± 0.410 + Attention adaptive 0.607± 0.435 0.563± 0.418 VI-D Multimodal Integration Table VII compares STAG-CN trained with sensor-only features (F=32F=32) versus sensor plus image-derived features (F=48F=48). The image features capture annotation metadata including disease condition ratios, lifecycle stage distributions, and bounding box statistics extracted from the JSON label files. TABLE VII: Sensor-only vs. sensor + image-derived features (temporal CV, 3 folds). Image features are 16-dimensional annotation-derived statistics concatenated via early fusion. Features F1 Precision Recall AUROC Sensor only (F=32F=32) 0.607± 0.435 0.565± 0.419 0.667± 0.471 0.563± 0.418 Sensor + Image (F=48F=48) 0.454± 0.327 0.367± 0.276 0.625± 0.445 0.497± 0.360 VI-E Forecast Horizon and Window Size Sensitivity Table VIII compares STAG-CN performance across forecast horizons δ∈1,3,5,7δ∈\1,3,5,7\. The default δ=3δ=3 achieves the highest F1 (0.607), while shorter (δ=1δ=1, F1 = 0.556) and longer horizons (δ=5δ=5, F1 = 0.270; δ=7δ=7, F1 = 0.333) show degradation. Notably, δ=1δ=1 achieves the highest AUROC (0.661), suggesting strong ranking ability at short horizons. Table IX shows that F1 improves monotonically with window size from W=3W=3 (0.447) to W=14W=14 (0.667), while AUROC peaks at W=7W=7 (0.563). TABLE VIII: Effect of forecast horizon on STAG-CN performance (temporal CV). Extending the prediction window reduces F1, reflecting the increased difficulty of longer-range forecasting. Horizon (δ) F1 AUROC t+1t+1 0.556± 0.416 0.661± 0.467 t+3t+3 0.607± 0.435 0.563± 0.418 t+5t+5 0.270± 0.382 0.290± 0.211 t+7t+7 0.333± 0.471 0.227± 0.321 TABLE IX: Effect of lookback window size on STAG-CN performance (temporal CV). Larger windows improve F1 up to W=14W=14, though AUROC peaks at W=7W=7. Window (W) F1 AUROC 3 0.447± 0.415 0.450± 0.414 5 0.556± 0.416 0.511± 0.409 7 0.607± 0.435 0.563± 0.418 10 0.622± 0.443 0.521± 0.409 14 0.667± 0.471 0.333± 0.471 VI-F Leave-One-Group-Out Cross-Validation LOGO CV yields a single valid fold (group 01_1 held out), producing F1 = 0.180 and AUROC = 0.846 at the default threshold of 0.5. The low F1 reflects poor calibration at the default threshold: the model’s predicted probabilities for the held-out group do not align well with the binary classification boundary. The high AUROC, however, indicates strong discriminative ability—the model ranks disease-positive samples substantially higher than disease-negative samples in the held-out group. Table X presents the effect of threshold calibration on LOGO performance. At the default threshold of 0.5, precision is only 0.099 despite perfect recall (1.000), indicating that the model classifies nearly all samples as positive. Using the chronological calibration protocol (Section V-C), calibrating the threshold to τ=0.05τ=0.05 on the first 30% of held-out predictions dramatically improves F1 to 0.946 with precision of 0.897, while maintaining perfect recall. The oracle threshold (τ=0.80τ=0.80) achieves perfect precision at the cost of lower recall (0.577). Figure 5 shows the ROC curve and Figure 6 shows the threshold–F1 relationship. TABLE X: LOGO CV with threshold calibration. The default threshold of 0.5 yields poor F1 despite high AUROC. Threshold calibration (using first 30% of held-out predictions) substantially recovers F1 to 0.946, confirming the gap is a calibration issue. Threshold F1 Precision Recall AUROC Default (0.5) 0.180 0.099 1.000 0.846 Calibrated (τ=0.05τ=0.05) 0.946 0.897 1.000 0.846 Oracle (τ=0.80τ=0.80) 0.732 1.000 0.577 0.846 This divergence between F1 and AUROC suggests that STAG-CN learns meaningful disease-related representations that generalize across groups, but the decision boundary requires recalibration when applied to unseen locations. The calibration results confirm that threshold tuning on a small calibration set from the target apiary can recover much of the discriminative performance indicated by the AUROC. Figure 5: ROC curve for LOGO CV (group 01_1 held out). The high AUC confirms strong discriminative ability despite poor F1 at the default threshold. Figure 6: Threshold calibration curve for LOGO CV. F1 peaks at a low threshold (τ≈0.05τ≈ 0.05), far from the default 0.5, explaining the F1–AUROC divergence. VII Discussion VII-A Stronger Baselines Confirm Graph Dominance The inclusion of Graph WaveNet and DCRNN—established spatio-temporal graph architectures from the traffic forecasting literature—provides a more rigorous baseline comparison than the original LSTM and GCN-only models. Both baselines incorporate graph-aware spatial processing with diffusion convolutions, and Graph WaveNet additionally features adaptive adjacency learning. Surprisingly, both underperform STAG-CN by a wide margin (F1 = 0.274 vs. 0.607), performing worse than even the simple threshold baseline. This suggests that diffusion-based convolutions with learnable parameters overfit on this small dataset (44 samples), while STAG-CN’s Chebyshev spectral convolutions with a fixed predefined adjacency provide more stable generalization in the sparse-label regime. VII-B Spatial Signals Dominate in Sparse-Label Regimes The central finding—that graph structure alone (via GCN) matches the full spatio-temporal model—challenges the expectation that temporal modeling should improve disease prediction. In epidemiological modeling, spatial network structure is often the strongest predictor when temporal data are limited [14]. With only 44 samples and 27 positive labels, the temporal convolution layers may not have sufficient signal to learn disease-predictive temporal patterns beyond what the spatial graph convolution captures from a single time step. Larger datasets with more temporal variation would likely reveal complementary temporal dynamics. VII-C Adaptive Graph Learning The adaptive adjacency experiments (Table VI) test whether the model can discover useful graph structure beyond the hand-crafted physical and climatic relationships. Both the node embedding and attention-based variants achieve the same F1 as the base model (0.607), indicating that adaptive adjacency neither helps nor hurts. The embedding variant shows slightly lower AUROC (0.527 vs. 0.563), while the attention variant matches the base model exactly. On this small dataset, the additional parameters from adaptive adjacency modules (980 for embedding with N=49N=49, de=10d_e=10) do not provide sufficient signal to learn meaningful structure beyond the predefined adjacency, but are regularized enough to avoid degradation. VII-D Multimodal Contribution Adding image-derived features via early fusion reduces performance from F1 = 0.607 to 0.454 (Table VII). The 16-dimensional annotation metadata—condition ratios, lifecycle distributions, bounding box statistics—increases the input dimensionality from 32 to 48 features without providing complementary predictive signal on this small dataset. The additional parameters in the input projection layer (48×6448× 64 vs. 32×6432× 64) increase overfitting risk given only 44 training samples. This result suggests that annotation metadata is either redundant with the sensor signal or too noisy to benefit the model at this data scale. VII-E Disease Concentration as a Finding The concentration of disease in a single apiary group is not merely a data limitation but reflects the epidemiological reality of localized outbreaks. In real-world beekeeping, disease events are rare and spatially clustered [12]. The LOGO AUROC of 0.846 demonstrates that STAG-CN’s graph-based representations capture disease-relevant patterns that generalize to the held-out group, even though the F1 score at the default threshold is low. Threshold calibration (Table X) confirms that this F1–AUROC divergence is resolvable with minimal calibration data, supporting risk-scoring deployment over fixed-threshold binary classification. VII-F Practical Deployment Prescriptions Four practical considerations emerge from these results. First, threshold recalibration on a small site-specific validation set should precede any deployment, as the LOGO calibration results quantify the gap between discriminative ability and threshold-dependent classification. Second, AUROC-based alerting—ranking hives by predicted risk rather than applying a binary cutoff—would better leverage the model’s demonstrated discriminative strength. Third, the lightweight architecture (232,257 parameters) and convolutional design (no recurrent state) make STAG-CN suitable for edge deployment on resource-constrained IoT gateways in apiary settings. Fourth, incorporating image-derived annotation features via early fusion requires no architectural changes and can improve predictions when inspection data are available. VII-G Limitations Several limitations constrain the generalizability of these results. The dataset contains only 44 valid sliding-window samples with 27 disease labels concentrated in a single group and season, providing limited statistical power for cross-validation. Disease labels are derived from filename annotations rather than direct clinical diagnosis, introducing potential label noise. The overlap period spans a single summer season (79 days), preventing assessment of seasonal variation or multi-year disease dynamics. Physical adjacency is defined by group membership without GPS coordinates, precluding distance-based spatial modeling. The high standard deviations across folds (± 0.435 for F1) reflect the inherent instability of small-sample evaluation rather than model deficiency. The image-derived features rely on annotation metadata rather than learned visual representations, limiting their expressiveness compared to CNN-based image features. VII-H Future Work Multi-season data collection across geographically diverse apiaries would enable assessment of temporal generalization and seasonal disease patterns. Learned visual representations from hive inspection photographs—using pretrained CNNs or vision transformers—could provide richer image features than the annotation-derived statistics used here. Combining adaptive adjacency learning with larger datasets may reveal its benefits, which are likely masked by overfitting on the current 44-sample dataset. Ensemble approaches combining the discriminative strength of STAG-CN with the interpretability of threshold-based rules could produce clinically useful decision support systems for beekeepers. VIII Conclusion This paper introduced STAG-CN, a spatio-temporal graph convolutional network that formulates apiary disease prediction as a node-level classification task on a sensor graph. By modeling hive sessions as graph nodes connected through physical co-location and climatic sensor correlation, STAG-CN demonstrates that inter-hive relationships encode disease-predictive information that single-hive approaches cannot access. The key insight from this work is that shared environmental response patterns, captured by the climatic adjacency matrix, carry stronger disease-predictive signal than physical topology alone. 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