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Spatio-Temporal Joint Graph Convolutional Networks for Traffic Forecasting

Chuanpan Zheng, Xiaoliang Fan, Shirui Pan, Haibing Jin, Zhaopeng Peng, Zonghan Wu, Cheng Wang, Philip S. Yu

arXiv:2111.13684v3cs.LGcs.AI

TL;DR

Traffic forecasting graphs often omit links between different nodes at different times and use adjacency that does not vary over time. STJGCN builds pre-defined and adaptive spatio-temporal joint graphs and processes multiple ranges; it is reported to be computationally efficient and to outperform 11 state-of-the-art baselines on five public traffic datasets.

  • Problem

    Prior traffic-forecasting graphs omit correlations between different nodes at different times, and their adjacency matrices commonly remain static despite dynamic spatio-temporal correlations.

    Source: §1 · pp. 1–2

  • Method

    STJGCN constructs pre-defined and adaptive spatio-temporal joint graphs, applies dilated causal joint graph convolution across multiple ranges, and aggregates ranges with attention.

    Source: §1 · p. 2

  • Results

    On five public traffic datasets, STJGCN is reported to be computationally efficient and to achieve the best performance against 11 state-of-the-art baseline methods.

    Source: §1 · p. 2, §6 · p. 12

  • Takeaways & Limitations

    The authors identify air-quality inference and taxi-demand prediction as potential applications for future investigation.

    Source: §6 · p. 12

    The adaptive graph assumes node relations can be modeled from latent attributes and their interactions, with nodes closer in latent space more likely to form links.

    Source: §4.2.2 · p. 4

Abstract

from arXiv · show

Recent studies have shifted their focus towards formulating traffic forecasting as a spatio-temporal graph modeling problem. Typically, they constructed a static spatial graph at each time step and then connected each node with itself between adjacent time steps to create a spatio-temporal graph. However, this approach failed to explicitly reflect the correlations between different nodes at different time steps, thus limiting the learning capability of graph neural networks. Additionally, those models overlooked the dynamic spatio-temporal correlations among nodes by using the same adjacency matrix across different time steps. To address these limitations, we propose a novel approach called Spatio-Temporal Joint Graph Convolutional Networks (STJGCN) for accurate traffic forecasting on road networks over multiple future time steps. Specifically, our method encompasses the construction of both pre-defined and adaptive spatio-temporal joint graphs (STJGs) between any two time steps, which represent comprehensive and dynamic spatio-temporal correlations. We further introduce dilated causal spatio-temporal joint graph convolution layers on the STJG to capture spatio-temporal dependencies from distinct perspectives with multiple ranges. To aggregate information from different ranges, we propose a multi-range attention mechanism. Finally, we evaluate our approach on five public traffic datasets and experimental results demonstrate that STJGCN is not only computationally efficient but also outperforms 11 state-of-the-art baseline methods.

1 INTRODUCTION

Prior spatio-temporal graph approaches omit links between different nodes at different times and commonly keep adjacency static across time. STJGCN constructs pre-defined and adaptive spatio-temporal joint graphs, processes multiple ranges, and outperforms 11 baselines on five public traffic datasets.

1 INTRODUCTION

  • The paper frames traffic forecasting as predicting future road-network traffic conditions from historical observations.It positions the work against graph approaches that model spatial neighborhoods and connect each node to itself across adjacent time steps.Source: §1 · p. 1
  • Existing spatio-temporal graphs omit correlations between different nodes at different times, while static pre-defined or adaptive adjacency matrices miss changing correlations.For example, a traffic jam may affect downstream roads in later hours, and correlations between residential and office areas can vary by time of day.Source: §1 · pp. 1–2
  • Pre-defined STJGs add cross-time spatio-temporal connections, while adaptive STJGs encode time features so adjacency can change across time steps.Together, the two graph types are designed to preserve comprehensive and dynamic spatio-temporal correlations.Source: §1 · p. 2
  • STJGCN is computationally efficient and achieves the best performance against 11 state-of-the-art baselines across five public traffic datasets.The method produces multi-step-ahead traffic predictions on road networks.Source: §1 · p. 2
  • Dilated causal spatio-temporal joint graph convolution layers capture dependencies across multiple ranges, and multi-range attention aggregates information from those ranges.The graph convolution layers are applied to both types of STJG.Source: §1 · p. 2

2 RELATED WORK

The related work describes graph convolution methods and their use in spatio-temporal forecasting. It identifies static correlations and omitted cross-time node links as limitations of graph-based forecasting approaches.

2.1 Graph Convolutional Networks

  • Graph convolution methods include spatial neighborhood aggregation and spectral-domain convolution, with examples including GraphSAGE, GAT, and ChebNet.The review notes that graph neural networks have been applied to time-series and spatio-temporal data, including traffic forecasting.Source: §2.1 · pp. 2–3

2.2 Spatio-Temporal Forecasting

  • Prior graph-based forecasting methods generally assume static node correlations and do not explicitly model correlations between different nodes at different time steps.The review also describes pre-defined adjacency based on prior knowledge and adaptive adjacency learned from data.Source: §2.2 · p. 3

3 PRELIMINARY

The preliminary section defines traffic forecasting on a road network as mapping measurements from historical time steps to measurements at future time steps.

3 PRELIMINARY

  • For N road-network sensors with C traffic measurements each, forecasting maps the previous P time steps of traffic conditions to the next Q time steps.At time t, the conditions are represented as X_t ∈ R^(N×C).Source: §3 · p. 3

4.1 Framework Overview

STJGCN combines joint-graph construction, joint graph convolution, and prediction modules. Its convolution and attention components model multiple spatio-temporal ranges before producing forecasts.

4.1 Framework Overview

  • The STJG construction module builds pre-defined and adaptive graphs to represent comprehensive and dynamic spatio-temporal correlations.This targets omitted cross-time connections and dynamic node correlations in earlier graph-based methods.Source: §4.1 · p. 3
  • STJGC applies a unified convolution operation to both graph types, while dilated causal STJGC captures dependencies across multiple neighborhood and time ranges.Source: §4.1 · p. 3
  • Multi-range attention aggregates information across ranges, and fully connected layers produce the prediction results.Source: §4.1 · p. 3

4.2 STJG Construction Module

The module pairs distance-based predefined STJGs with adaptive STJGs to represent comprehensive spatio-temporal correlations, including correlations that vary over time.

4.2 STJG Construction Module

  • The construction module combines predefined and adaptive STJGs to represent comprehensive and dynamic spatio-temporal correlations among nodes.Source: §4.2 · p. 3

4.2.1 Pre-defined Spatio-Temporal Joint Graph

  • Predefined STJGs add distance-weighted links between different nodes at different time steps, extending spatial and self-temporal connections to any pair of time steps.Source: §4.2.1 · pp. 3–4
  • Predefined adjacency weights below a threshold are removed to eliminate weak connections and control graph sparsity.Source: §4.2.1 · p. 4

4.2.2 Adaptive Spatio-Temporal Joint Graph

  • Adaptive STJGs use latent node attributes combined with time-of-day and day-of-week embeddings, then threshold and normalize time-varying adjacency matrices for cross-time links.Source: §4.2.2 · p. 4

4.3 Dilated Causal STJGC Module

The module applies spatio-temporal joint graph convolution to predefined and adaptive STJGs, then stacks causal dilated layers to capture dependencies at multiple ranges.

4.3.1 Spatio-Temporal Joint Graph Convolution (STJGC)

  • STJGC applies graph convolution to both types of STJG, unifying information propagation across spatial, temporal, and spatio-temporal connections.Source: §4.3.1 · p. 5
  • For predefined STJGs, each update combines spatial neighbors at t with temporal and spatio-temporal neighborhood information from earlier t−k steps across a configurable K-step kernel.Source: §4.3.1 · p. 5
  • Adaptive STJGC considers both time directions, then a node- and channel-wise gate fuses features from predefined and adaptive STJGs.Source: §4.3.1 · p. 5

4.3 Dilated Causal STJGC Module

  • The prediction module uses multi-range attention to aggregate STJGC layer outputs before fully connected layers produce predictions.Source: Figure 3 · p. 6

4.3.2 Dilated Causal STJGC Layers

  • Dilated causal layers skip input steps while preserving causality; deeper layers span longer ranges and higher-order neighborhoods, with the last reaching 4-hop neighborhoods across all P input steps.Source: §4.3.2 · p. 6

4.4 Prediction Module

The prediction module combines information from multiple spatio-temporal ranges, then produces forecasts for each horizon using independent fully connected layers and a combined MAE–MAPE loss.

4.4.1 Multi-Range Attention

  • Multi-range attention aggregates information from STJGC layers, whose smaller and larger ranges represent local and global dependencies.The mechanism accounts for differing importance across ranges.Source: §4.4.1 · p. 6
  • Attention aggregates features from multiple ranges into node representations, with shared parameters applied to all nodes in parallel.The resulting output is Y ∈ R^N×d.Source: §4.4.1 · p. 7

4.4.2 Independent Fully-Connected Layers

  • Independent two-layer fully connected networks generate predictions for each of the Q forecasting horizons.The paper motivates separate networks because traffic at different time steps may exhibit different properties.Source: §4.4.2 · p. 7

4.4.3 Loss Function

  • The loss combines MAE and MAPE, balanced by β.The paper motivates MAPE as more relevant to small-value predictions, while MAE treats prediction values equally.Source: §4.4.3 · p. 7

4.5 Complexity Analysis

The analysis gives complexity estimates for adaptive STJG construction, dilated STJGC operations, and the prediction module, identifying where computation scales with graph size and forecast horizon.

4.5 Complexity Analysis

  • Adaptive STJG construction costs O(Nd^2 + N^2d), or O(N^2) when d is treated as constant; restricting computation to pre-defined connected edges is suggested to mitigate scale costs.The pairwise embedding computation drives the quadratic node-count term.Source: §4.5 · p. 7
  • Each dilated STJGC operation costs O(K(|E|d + Nd^2)), with complexity mainly dependent on the number of graph edges |E|.Each node aggregates information from its edge-defined neighborhood.Source: §4.5 · p. 7
  • The prediction module costs O(N(Md + Qd^2)), with its fully connected layers making complexity highly related to the forecast horizon Q.The module uses Q independent fully connected layers.Source: §4.5 · p. 7

5 EXPERIMENTS

The experiments use five highway traffic datasets and standard forecasting metrics, with a fixed historical-to-future horizon setup and comparisons against 11 baselines across two model families.

5.1 Datasets

  • The five datasets comprise four PeMS datasets and Seattle-Loop; the experiments predict flow on PeMS and speed on Seattle-Loop.PeMS data are aggregated to five-minute intervals; Seattle-Loop contains five-minute speed readings from 323 Greater Seattle detectors during 2015.Source: §5.1 · p. 7

5.2.1 Evaluation Metrics

  • Evaluation uses mean absolute error (MAE), root mean squared error (RMSE), and mean absolute percentage error (MAPE).The metrics are defined for predictions across nodes and forecast steps.Source: §5.2.1 · pp. 7–8

5.2.2 Experimental Settings

  • The models use 12 historical time steps to predict the next 12; experiments use chronological 60/20/20 train-validation-test splits and report means and standard deviations over five runs.Training uses Adam with initial learning rate 0.001 and batch size 64 for up to 200 epochs, selecting the best validation model.Source: §5.1 · p. 7, §5.2.2 · p. 8

5.2.3 Baseline Methods

  • Eleven baselines span time-series models and spatio-temporal graph neural networks, including VAR, DCRNN, STGCN, and Graph WaveNet.The listed methods include both traditional time-series and graph-based approaches.Source: §5.2.3 · p. 8

5.3 Experimental Results

STJGCN outperforms 11 baselines across five datasets, while ablations and parameter studies examine its graph connections, dynamic modeling, multi-range design, and hyperparameter trade-offs. It also performs well across forecasting horizons and balances accuracy with model size and computation time.

5.3.1 Overall Comparison

  • STJGCN performs best on all metrics across all datasets, improving 1.4%˜7.7% over the second-best results.The overall comparison is against 11 baseline methods.Source: §5.3.1 · pp. 8–9, Table 3 · p. 9

5.3.2 Ablation Study

  • Removing spatio-temporal connections or time-varying graph modeling worsens performance, supporting both cross-time links and dynamic correlations.The static-graph variant omits time features when generating its adaptive adjacency matrix.Source: §5.3.2 · p. 9
  • Ablations favor multiple ranges, attention, independent horizon-specific prediction layers, and combining predefined and adaptive graphs with gating fusion.Adaptive-only graphs also perform promisingly when graph structure is unavailable.Source: §5.3.2 · p. 9

5.3.3 Parameter Study

  • Performance is not strongly sensitive to graph sparsity; excessive sparsity can remove related nodes, so thresholds are selected by dataset.The selected thresholds are δpdf = δadt = 0.5 for PeMSD4 and δpdf = 0.5, δadt = 0.3 for PeMSD8.Source: §5.3.3 · p. 10
  • Widths above 64 degrade performance; kernels of 2–3 suffice while 1 misses temporal links, and larger β trades lower MAPE for higher MAE.Selected kernel sizes are K = 3 for PeMSD4 and K = 2 for PeMSD8.Source: §5.3.3 · pp. 10, 12

5.3.4 Performance Comparison at Each Horizon

  • Graph WaveNet performs well at short horizons and GMAN at longer ones, while STJGCN is best at almost all horizons across three metrics on both datasets.The comparison covers PeMSD4 and PeMSD8.Source: Figure 6 · p. 11, Figure 7 · p. 11, §5.3.4 · p. 12

5.3.5 Model Size and Computation Time

  • Across PeMS datasets, STJGCN has fewer parameters than most and trains faster except STGCN; on Seattle-Loop, it trains faster than GMAN and Z-GCNETs.For inference, it is among the most efficient on PeMS and slower only than STSGCN and AGCRN on Seattle-Loop.Source: Table 6 · p. 12, §5.3.5 · p. 12

6 CONCLUSION

The conclusion presents STJGCN as a traffic forecaster that models comprehensive and dynamic spatio-temporal correlations while aggregating multiple information ranges. Across five public traffic datasets, it reports high computational efficiency and outperforms 11 state-of-the-art baselines.

6 CONCLUSION

  • STJGCN combines comprehensive and dynamic spatio-temporal correlations with multi-range information aggregation for multi-step road-traffic forecasting.The paper identifies air-quality inference and taxi-demand prediction as possible future applications.Source: §6 · p. 12
  • On five public traffic datasets, STJGCN reports high computational efficiency and outperforms 11 state-of-the-art baselines.Source: §6 · p. 12
  • The authors identify air-quality inference and taxi-demand prediction as potential future applications and plan to investigate them.Source: §6 · p. 12
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