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Adaptive Graph Convolutional Recurrent Network for Traffic Forecasting

Lei Bai, Lina Yao, Can Li, Xianzhi Wang, Can Wang

arXiv:2007.02842v2cs.LGstat.ML

TL;DR

Traffic forecasting requires modeling complex temporal and spatial dependencies, but existing approaches emphasize shared patterns and often rely on predefined graphs. The paper introduces NAPL and DAGG within AGCRN to learn node-specific patterns and infer spatial dependencies from data. On two real-world datasets, AGCRN significantly outperforms state-of-the-art models without predefined spatial graphs.

  • Problem

    Traffic forecasting must capture complex temporal and spatial dependencies across correlated series, while shared parameters and predefined graphs limit node-specific modeling.

  • Method

    AGCRN combines Node Adaptive Parameter Learning for node-specific parameters with Data Adaptive Graph Generation for data-driven spatial dependencies and recurrent forecasting.

  • Results

    AGCRN outperforms state-of-the-art traffic forecasting models by a significant margin on two real-world datasets without predefined spatial graphs.

  • Takeaways & Limitations

    Adaptive modules support learning node-specific spatial and temporal correlations and inferring inter-dependencies from data for correlated time-series forecasting.

  • Takeaways & Limitations

    The authors identify future work in validating AGCRN on more time-series tasks and adapting NAPL and DAGG to additional GCN-based forecasting models.

Abstract

from arXiv · show

Modeling complex spatial and temporal correlations in the correlated time series data is indispensable for understanding the traffic dynamics and predicting the future status of an evolving traffic system. Recent works focus on designing complicated graph neural network architectures to capture shared patterns with the help of pre-defined graphs. In this paper, we argue that learning node-specific patterns is essential for traffic forecasting while the pre-defined graph is avoidable. To this end, we propose two adaptive modules for enhancing Graph Convolutional Network (GCN) with new capabilities: 1) a Node Adaptive Parameter Learning (NAPL) module to capture node-specific patterns; 2) a Data Adaptive Graph Generation (DAGG) module to infer the inter-dependencies among different traffic series automatically. We further propose an Adaptive Graph Convolutional Recurrent Network (AGCRN) to capture fine-grained spatial and temporal correlations in traffic series automatically based on the two modules and recurrent networks. Our experiments on two real-world traffic datasets show AGCRN outperforms state-of-the-art by a significant margin without pre-defined graphs about spatial connections.

1 Introduction

Traffic forecasting must model complex temporal and spatial dependencies across heterogeneous traffic series. AGCRN addresses this with node-specific parameter learning and data-adaptive graph generation, achieving a significant margin over state-of-the-art models without predefined spatial graphs.

  • Traffic forecasting predicts future traffic-system status and supports traffic scheduling and management amid growing urban mobility and sustainability challenges.
  • Traffic series contain complex intra-dependencies over time and inter-dependencies across correlated sources, challenging traditional time-series models.
  • Deep-learning methods model temporal dependencies with recurrent or convolutional modules and spatial correlations with graph convolutional networks.
  • Shared parameters and predefined graphs limit fine-grained modeling because traffic series can exhibit diverse, dissimilar, or contradictory patterns.
  • NAPL learns node-specific patterns, while DAGG infers inter-dependencies from data; together they form AGCRN for adaptive spatial-temporal forecasting.
  • AGCRN outperforms state-of-the-art models by a significant margin on two real-world datasets, while ablations demonstrate the effectiveness of both adaptive modules.

2 Related Work

Related work models correlated time series primarily with recurrent or convolutional temporal methods and uses spatial assumptions or graph structures for traffic forecasting. GCNs generalize CNNs to graph-structured data, while this paper targets evolving streams without a given graph.

  • Correlated time series prediction: Deep-learning approaches commonly use LSTM or GRU to model temporal dynamics in correlated time series.
  • Correlated time series prediction: Temporal convolutional networks are used to process very long correlated time series, but such models normally require massive training samples because of many trainable parameters.
  • GCN based Traffic forecasting: Traffic forecasting additionally models spatial correlations among series from different spaces, regions, or sensors.
  • GCN based Traffic forecasting: CNN-based traffic methods may assume grid-partitioned cities, an assumption that does not always hold.
  • Graph Convolutional Networks: GCNs generalize CNNs to graph-structured data and commonly learn node representations by integrating features from local neighbors using a given graph.
  • Graph Convolutional Networks: This work differs by modeling dynamically evolving streams across spatial and temporal dimensions without a given graph structure.

3 Methodology

The methodology formulates multi-step traffic forecasting over correlated series and builds AGCRN by combining graph convolution, node-adaptive parameters, data-adaptive graph generation, and recurrent processing.

  • 3.1 Problem Definition: Multi-step forecasting maps the past T steps of N correlated traffic series to the next τ steps.The formulation represents traffic sources as graph nodes and can incorporate an adjacency matrix describing proximity or similarity.
  • 3.2 Node Adaptive Parameter Learning: Standard GCNs share weights across nodes, but traffic series can exhibit diverse, dissimilar, or reverse patterns, motivating node-specific parameters.The paper notes that directly assigning parameters to every node would create Θ ∈ R^N×C×F and risk excessive optimization size and overfitting.
  • 3.2 Node Adaptive Parameter Learning: NAPL factorizes node-specific weights through a node-embedding matrix and a smaller shared weight pool, generating each node’s parameters from its embedding.The same adaptive operation is applied to the bias, producing the NAPL-enhanced GCN.
  • 3.3 Data Adaptive Graph Generation: DAGG learns node embeddings and infers hidden inter-dependencies from data, normalizing the resulting adaptive matrix for graph convolution.It directly generates the normalized graph-convolution factor instead of repeatedly constructing an adjacency and Laplacian matrix.
  • 3.4 Adaptive Graph Convolutional Recurrent Network: AGCRN integrates NAPL-GCN, DAGG, and GRU-like recurrence to model node-specific spatial-temporal correlations end-to-end.The recurrent formulation uses shared embedding parameters across GCN blocks, acting as a regularizer for embedding consistency.
  • 3.4 Adaptive Graph Convolutional Recurrent Network: Stacked AGCRN layers encode historical data and directly project representations to the next τ steps, avoiding sequential output generation.The model jointly optimizes multi-step predictions with L1 loss using back-propagation and Adam.

4 Experiments

Experiments on two real-world traffic datasets evaluate AGCRN against representative forecasting models and analyze its adaptive modules, graph generation, embedding dimension, and computation cost. AGCRN achieves strong overall performance, while ablations support the contributions of NAPL and DAGG and model analysis identifies trade-offs in embedding size and parameters.

  • Experimental Setup: Experiments use PeMSD4 and PeMSD8 traffic-flow datasets, with chronological 6:2:2 train-validation-test splits and one hour of history predicting the next hour.PeMSD4 contains 307 loop detectors in the San Francisco Bay Area; PeMSD8 contains 170 loop detectors in the San Bernardino area.
  • Overall Comparison: AGCRN is compared with widely used baselines and state-of-the-art models using MAE, RMSE, and MAPE averaged over 12 prediction horizons.The comparison includes historical average, VAR, GRU-ED, DSANet, and other representative methods.
  • Overall Comparison: More than 5% relative improvements in MAE and MAPE are reported over existing best results on both PeMSD4 and PeMSD8.AGCRN achieves the best performance for almost all PeMSD4 horizons except the first step, and its performance deteriorates more slowly than other GCN-based models.
  • Ablation Study: NAPL-GCGRU generally outperforms GCGRU, while AGCCRN-I outperforms DAGG-GCGRU, supporting node-specific pattern learning and adaptive spatial-correlation inference.The ablation study is conducted on PeMSD4 and compares variants that separately replace traditional GCN components with NAPL or DAGG.
  • Ablation Study: DAGG-GCGRU improves GCGRU, AGCRN-I beats NAPL-GCGRU, and AGCRN achieves the best performance, supporting joint use and shared node embeddings.The results also report that pre-defining an adjacent matrix is not necessary for the tested approach.
  • Model Analysis: AGCRN performs relatively well across tested embedding dimensions and is best at dimension 10, while excessively small or large dimensions weaken performance.Larger embeddings can improve learned spatial correlations but increase NAPL parameters, making optimization harder and potentially causing over-fitting.
  • Computation Cost: With embedding dimension 10, AGCRN has five times more parameters than DCRNN but trains slightly faster, and its computation cost is characterized as moderate.STGCN trains fastest, while adding spatial and temporal attention mechanisms to STGCN requires more parameters and training time.

5 Discussion

The proposed adaptive modules may extend beyond traffic forecasting to other multivariate or correlated time-series tasks. Future work targets broader validation across tasks and adaptation to additional GCN-based traffic models.

  • The adaptive modules and AGCRN may be adapted separately or jointly to multivariate and correlated time-series prediction tasks beyond traffic forecasting.
  • The approach infers inter-dependencies from data when graph-based prediction models cannot easily pre-define a graph.
  • Future scalability evaluation should cover more time-series prediction tasks and adaptation of NAPL and DAGG to additional GCN-based traffic forecasting models.

6 Conclusion

The paper concludes that AGCRN combines node-adaptive parameter learning and data-adaptive graph generation to model fine-grained spatial and temporal correlations without a pre-defined graph. Experiments support the effectiveness of AGCRN and both adaptive modules.

  • AGCRN combines NAPL and DAGG with recurrent modeling to capture node-specific spatial and temporal correlations automatically without a pre-defined graph.
  • Extensive multi-step traffic forecasting experiments demonstrate the effectiveness of AGCRN and both proposed adaptive modules.
  • The conclusion identifies learning node-specific patterns as essential for understanding correlated time-series data.

Broader Impact

The work connects adaptive traffic forecasting with higher-level traffic scheduling and broader correlated time-series analysis. It also identifies a potential fairness concern for ride-sharing platforms when predicted high-demand areas receive priority.

  • The adaptive modules are presented as relevant to broader analysis of dynamic, interdependent time-series data across social and business applications.
  • A potential negative impact is unfair ride-sharing allocation when platforms prioritize predicted high-demand areas under constrained cab supply.

A Appendix

The appendix supports reproducibility by providing code and datasets as supplementary information. It also covers dataset statistics, evaluation metrics, implementation details, and additional results.

  • Code and datasets are submitted as supplementary information to support reproducibility of the reported results.
  • The supplementary material presents dataset statistics, evaluation metrics, implementation details, and more results.

A.1 Datasets Statistics

The experiments use PeMSD4 and PeMSD8 traffic-flow datasets measured by road traffic sensors. Traffic sensors are modeled as graph nodes, while AGCRN infers spatial proximity without a pre-defined adjacency matrix.

  • PeMSD4 and PeMSD8 contain traffic-flow measurements collected by road traffic sensors.
  • Each traffic sensor corresponds to a graph node in the traffic-forecasting formulation.
  • AGCRN infers spatial proximity from data through DAGG rather than requiring a pre-defined adjacency matrix.

A.2 Evaluation Metrics

The study evaluates predictive models using three metrics based on predicted values, ground-truth traffic, and observed-sample indices: MAE, RMSE, and MAPE.

  • Three evaluation metrics measure predictive-model performance: Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Mean Absolute Percentage Error (MAPE).
  • The metric definitions use predicted values, ground-truth traffic, and the indices of observed samples.
  • The evaluation setup represents traffic across all nodes at each time step.

A.3 Implementation Details

The implementation compares AGCRN with statistical, recurrent, attention, and graph-convolutional baselines using specified training configurations and horizon-wise evaluation. On PeMSD8, AGCRN has the strongest reported performance, particularly for long-term prediction, with slower deterioration than other GCN-based models.

  • Baseline models: The comparison includes HA, VAR, GRU-ED, DSANet, DCRNN, STGCN, ASTGCN, and STSGCN baselines.The baselines span historical averaging, vector autoregression, recurrent models, attention-based models, and graph-convolutional architectures.
  • AGCRN implementation: AGCRN stacks two layers to capture node-specific spatial and temporal dynamics, then maps the final recurrent representation to predictions for all horizons.The hidden-unit and batch-size settings are both 64.
  • Training procedure: Deep learning models are optimized with Adam for 100 epochs with early stopping based on validation loss and patience of 15.
  • Evaluation comparison: Figure 5 compares prediction performance at each horizon on PeMSD8; STSGCN is omitted because its step-wise results are unavailable, and HA is omitted because performance is constant across horizons.
  • Evaluation comparison: AGCRN outperforms existing baselines by a significant margin, especially for long-term predictions, and deteriorates more slowly than other GCN-based models.The passage reports similar observations beyond the displayed PeMSD8 comparison, but the supplied text does not complete that statement.
  • Visualization: Figures 6 and 7 provide traffic forecasting visualizations.
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