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Spatiotemporal-aware Trend-Seasonality Decomposition Network for Traffic Flow Forecasting
Lingxiao Cao, Bin Wang, Guiyuan Jiang, Yanwei Yu, Junyu Dong
TL;DR
Traffic forecasting needs models that capture periodic temporal structure, global spatial interactions, and node-level trend-seasonality patterns. STDN combines spatio-temporal embeddings with dynamic graph learning and trend-seasonality decomposition, then uses an encoder-decoder for prediction. Across three real-world datasets, it reports superior performance over existing models and releases the inner-city JiNan dataset.
Problem
Existing traffic forecasting methods incompletely model long- and short-period synergy, global node interactions, and interactions overlooked by node-wise trend-seasonality decomposition.
Method
STDN learns spatio-temporal embeddings and dynamic global node relationships, disentangles trend-cyclical and seasonal components, and processes them through an encoder-decoder.
Results
STDN demonstrates superior performance over existing models across three real-world traffic datasets, with module effectiveness verified through ablation studies.
Takeaways & Limitations
The released JiNan dataset adds inner-city traffic dynamics to traffic-forecasting evaluation scenarios.
Takeaways & Limitations
The decomposition assumes nearby times and locations have similar trends while distinct times and locations exhibit unique traffic patterns.
Abstract
from arXiv · showhide
Traffic prediction is critical for optimizing travel scheduling and enhancing public safety, yet the complex spatial and temporal dynamics within traffic data present significant challenges for accurate forecasting. In this paper, we introduce a novel model, the Spatiotemporal-aware Trend-Seasonality Decomposition Network (STDN). This model begins by constructing a dynamic graph structure to represent traffic flow and incorporates novel spatio-temporal embeddings to jointly capture global traffic dynamics. The representations learned are further refined by a specially designed trend-seasonality decomposition module, which disentangles the trend-cyclical component and seasonal component for each traffic node at different times within the graph. These components are subsequently processed through an encoder-decoder network to generate the final predictions. Extensive experiments conducted on real-world traffic datasets demonstrate that STDN achieves superior performance with remarkable computation cost. Furthermore, we have released a new traffic dataset named JiNan, which features unique inner-city dynamics, thereby enriching the scenario comprehensiveness in traffic prediction evaluation.
Introduction
Traffic forecasting must capture complex spatial and temporal dynamics, but existing methods inadequately model periodicity synergy, global interactions, and node-level trend-seasonality structure. STDN addresses these gaps with spatio-temporal embeddings, dynamic graph learning, and decomposition.
- Traffic forecasting uses historical flow data and road topology to predict future traffic variations for intelligent transportation applications.
- STGNNs improve traffic forecasting over statistical time-series and shallow machine-learning methods by modeling spatio-temporal dynamics.
- Existing methods often model temporal features without explicitly linking long- and short-period periodicities, while static distance-based graphs miss global node interactions.
- Node-wise trend-seasonality decomposition can improve representations, but ignoring interactions among global nodes diminishes GNN-learned node representations.
- STDN learns temporal and spatial embeddings, dynamic global node relationships, and disentangled trend-cyclical and seasonal components processed by an encoder-decoder.
- Experiments cover three real-world datasets, compare STDN with competing baselines, verify modules through ablation, and introduce the inner-city JiNan dataset.
Related Works
Prior traffic forecasting work uses graph, attention, and decomposition-based methods to model spatial and temporal dependencies. However, existing approaches have not fully exploited spatio-temporal embeddings within traffic sequences.
- GCN-based models combine graph convolution with sequential data, while adaptive graphs address limitations of predefined traffic-network connectivity.
- Attention-based models capture global temporal correlations and increasingly integrate spatial correlations with temporal dynamics.
- Attention-based approaches have not fully leveraged spatio-temporal embeddings within traffic sequence data.
- Decomposition-based methods separate traffic sequences into trend-cyclical and seasonal components, with related models also using diffusion, intrinsic, or delay signals.
Problem Definition
The paper represents a traffic network as a directed sensor graph and formulates forecasting as mapping historical node time series and topology to future traffic values.
- A traffic network is a directed graph G = {V, E, A}, where nodes are sensors, edges encode connectivity, and A is the adjacency matrix.
- Traffic forecasting predicts future traffic time-series values from historical traffic time series and road topology.
- The historical signal tensor X ∈ R^T×N×C records T time steps, N nodes, and C node-attribute dimensions.
- The forecasting function maps [X1, X2, . . . , XT ; G] to predictions for the subsequent T′ time steps.
Methodology
STDN uses dynamic graph learning to model time-varying higher-order node relationships and produces processed node sequences by aggregating graph-neighbor states across layers and time.
- STDN comprises three principal modules for traffic-flow forecasting.
- Dynamic relationship graph learning models higher-order spatio-temporal relationships among all traffic nodes beyond simple distance-based connectivity.
- The graph-learning module uses time-slot, starting-node, and ending-node embeddings together with a learnable core tensor.
- The resulting tensor A ∈ R^Nt×Ns×Ne encodes high-order connectivity among global nodes across time steps.
- Dynamic graph convolution updates node hidden states by aggregating neighbors through time-specific weighted links and layer parameters.
- The graph-convolution process produces final processed sequence data HL ∈ R^T×N×D.
Module 2: Spatio-Temporal Embeddings Learning
The module learns temporal embeddings from time-of-day and weekly information and spatial embeddings from the road graph, then combines them into refined spatio-temporal representations for each node and time.
- Temporal embedding: Temporal context embeddings encode time-of-day and day-of-week features to capture multi-resolution traffic periodicities.The initial temporal representation is refined with a bias-free MLP using ReLU and sigmoid activations.
- Spatial embedding: The normalized graph Laplacian provides eigenvalues and eigenvectors for constructing an initial spatial embedding from the 32 smallest nontrivial eigenvectors.The eigenvectors are selected to capture global information from road-network structure.
- Spatial embedding: A bias-free MLP transforms the initial spatial embedding into an N×D representation using trainable parameters and ReLU activation.The resulting spatial embedding is used in subsequent model stages.
- Embedding fusion: Spatial and temporal embeddings are broadcast across time and nodes, respectively, then combined to form refined spatio-temporal information for every node at each time.The combined embedding has shape T×N×D and uses sine and ReLU-based transformations.
- Embedding fusion: The sine transformation normalizes embedding values and helps represent nonlinear changes before fusion with traffic sequences.The passage describes normalization and nonlinear-change modeling as benefits of the sine function.
Module 3: Trend-Seasonality Decomposition
The decomposition module uses spatio-temporal context to separate each node’s traffic representation into trend-cyclical and seasonal components, assuming nearby times and locations have similar trends.
- Decomposition design: The module disentangles traffic flow into distinct trend-cyclical and seasonal components using spatio-temporal embeddings.The resulting representations are adjusted for the forecasting task.
- Component extraction: The trend-cyclical component is obtained by elementwise multiplying node hidden states with the spatio-temporal embedding, while the residual becomes the seasonal component.The formulation is X_t = H_L ⊙ M and X_s = H_L − X_t.
- Component extraction: The method assumes nearby times and locations yield similar trends, whereas distinct times and locations exhibit unique traffic patterns.This is presented as a mild assumption underlying the trend extraction.
Encoder-Decoder Architecture
The encoder-decoder architecture processes the separated trend and seasonal representations with GRU encoders and a Transformer decoder, while bottleneck blocks reduce temporal and spatial complexity.
- Encoding: GRU encoders separately process the trend and seasonal components to extract deeper spatio-temporal features.The outputs are denoted Y_t and Y_s and correspond to the two decomposed components.
- Encoding: The encoded trend and seasonal outputs are combined by elementwise summation to produce the final representation.The combined output is denoted Y and has shape T×N×D.
- Decoding: A Transformer decoder uses multi-head attention by projecting queries, keys, and values into h d-dimensional subspaces and executing attention in parallel.The architecture is selected for its multi-head attention mechanism during decoding.
- Complexity: Bottleneck Transformer Blocks are incorporated to reduce both temporal and spatial complexity.The dataset-statistics table is identified as Table 1, but the supplied passages do not provide its values.
- Decoding: Predicted temporal embeddings are expanded across nodes and concatenated with the preceding bottleneck-block output to guide decoder modeling of high-order time-space dynamics.The predicted embedding is maintained with T = T′ before expansion across N nodes.
Baseline Methods
The evaluation compares STDN with traditional statistical and machine-learning predictors as well as deep spatio-temporal models spanning recurrent, convolutional, graph, and attention-based approaches.
- Evaluation setup: The study evaluates STDN against a diverse range of established baselines.The supplied passage introduces the comparison set but does not report comparative metric values.
- Traditional and sequence baselines: Traditional baselines include historical average, ARIMA, VAR, support vector regression, and LSTM.LSTM models temporal dependencies but does not account for spatial correlations.
- Graph-based models: Graph-based baselines include DCRNN, STGCN, and GWNet, which model traffic using diffusion, graph, temporal, or dilated convolutions.GWNet additionally introduces a self-adaptive adjacency matrix.
Evaluation Metrics and Experimental Settings
The experiments evaluate traffic forecasting with MAE, RMSE, and MAPE across real-world datasets, using graph- and grid-based baselines plus STDN variants. STDN reports state-of-the-art performance, while ablations assess the contributions of its embeddings, dynamic graph learning, and decomposition.
- Evaluation Metrics: MAE, RMSE, and MAPE quantify the performance of the evaluated traffic forecasting methods.
- Experimental Comparison: The experimental comparison includes graph-based and grid-based baselines, with best and second-best results marked separately.
- Performance Comparison: STDN achieves state-of-the-art performance, particularly on the PeMS04 and JiNan datasets.
- Ablation Study: The ablation study removes temporal embedding, spatial embedding, spatio-temporal embedding, dynamic relationship graph learning, or the proposed decomposition to evaluate each component.
- Ablation Study: The full STDN configuration consistently outperforms its variants, while removing dynamic graph learning or spatiotemporal-aware decomposition reduces performance.
Parameter Sensitivity Study
The sensitivity study varies decoder depth and feature dimensionality, showing that performance stabilizes at two decoder layers and peaks at dataset-specific feature sizes. Efficiency experiments further report faster training, inference, and convergence for STDN than the compared models.
- Parameter Sensitivity: Performance improves as decoder layers increase but stabilizes at 2 layers.The tested layer range is [1, 2, 3, 4].
- Parameter Sensitivity: Optimal performance uses 128 features on PeMS04 and 96 features on PeMS07.The tested feature range is [32, 64, 96, 128, 160].
- Parameter Sensitivity: Increasing features can improve representation of complex traffic patterns, but excessive features may introduce noise and degrade performance.
- Model Efficiency: STDN trains and infers faster than DMSTGCN, SSTBAN, and STWave in the reported efficiency comparison.The comparison uses average training time per epoch and inference time.
- Model Efficiency: STDN reaches its lowest reported MAE at epoch 19, whereas STWave reaches its best performance at epoch 100 with higher MAE.
- Computational Complexity: The encoder-decoder module has computational complexity O(TD+LND), while graph-Laplacian eigenvalue and eigenvector computation is handled before training.
Conclusion
STDN learns disentangled traffic-flow representations using spatio-temporal embeddings and demonstrates superior performance across three real-world datasets. The JiNan dataset broadens traffic-forecasting evaluation scenarios with inner-city dynamics.
- STDN employs spatio-temporal embeddings to learn disentangled representations of traffic flow.
- STDN demonstrates superior performance over existing models across three real-world datasets.
- The released JiNan dataset enriches scenario comprehensiveness in traffic-forecasting evaluations.