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Virtual Nodes Improve Long-term Traffic Prediction

Xiaoyang Cao, Dingyi Zhuang, Jinhua Zhao, Shenhao Wang

TL;DR

This work tackles the limitations of ST-GNNs for long-term traffic prediction caused by limited global information and over-squashing. It introduces virtual nodes connected to all real nodes and a semi-adaptive adjacency that blends distance-based structure with learnable, task-specific relations, enabling global information aggregation in a single layer. Empirical results on a San Diego traffic dataset show notable improvements in long-horizon accuracy and layer-wise sensitivity, along with explainability via adjacency heatmaps highlighting key intersections. The approach promises practical benefits for urban traffic management and lays groundwork for future enhancements such as time-varying adjacency and scalability.

Abstract

Effective traffic prediction is a cornerstone of intelligent transportation systems, enabling precise forecasts of traffic flow, speed, and congestion. While traditional spatio-temporal graph neural networks (ST-GNNs) have achieved notable success in short-term traffic forecasting, their performance in long-term predictions remains limited. This challenge arises from over-squashing problem, where bottlenecks and limited receptive fields restrict information flow and hinder the modeling of global dependencies. To address these challenges, this study introduces a novel framework that incorporates virtual nodes, which are additional nodes added to the graph and connected to existing nodes, in order to aggregate information across the entire graph within a single GNN layer. Our proposed model incorporates virtual nodes by constructing a semi-adaptive adjacency matrix. This matrix integrates distance-based and adaptive adjacency matrices, allowing the model to leverage geographical information while also learning task-specific features from data. Experimental results demonstrate that the inclusion of virtual nodes significantly enhances long-term prediction accuracy while also improving layer-wise sensitivity to mitigate the over-squashing problem. Virtual nodes also offer enhanced explainability by focusing on key intersections and high-traffic areas, as shown by the visualization of their adjacency matrix weights on road network heat maps. Our advanced approach enhances the understanding and management of urban traffic systems, making it particularly well-suited for real-world applications.

Virtual Nodes Improve Long-term Traffic Prediction

TL;DR

This work tackles the limitations of ST-GNNs for long-term traffic prediction caused by limited global information and over-squashing. It introduces virtual nodes connected to all real nodes and a semi-adaptive adjacency that blends distance-based structure with learnable, task-specific relations, enabling global information aggregation in a single layer. Empirical results on a San Diego traffic dataset show notable improvements in long-horizon accuracy and layer-wise sensitivity, along with explainability via adjacency heatmaps highlighting key intersections. The approach promises practical benefits for urban traffic management and lays groundwork for future enhancements such as time-varying adjacency and scalability.

Abstract

Effective traffic prediction is a cornerstone of intelligent transportation systems, enabling precise forecasts of traffic flow, speed, and congestion. While traditional spatio-temporal graph neural networks (ST-GNNs) have achieved notable success in short-term traffic forecasting, their performance in long-term predictions remains limited. This challenge arises from over-squashing problem, where bottlenecks and limited receptive fields restrict information flow and hinder the modeling of global dependencies. To address these challenges, this study introduces a novel framework that incorporates virtual nodes, which are additional nodes added to the graph and connected to existing nodes, in order to aggregate information across the entire graph within a single GNN layer. Our proposed model incorporates virtual nodes by constructing a semi-adaptive adjacency matrix. This matrix integrates distance-based and adaptive adjacency matrices, allowing the model to leverage geographical information while also learning task-specific features from data. Experimental results demonstrate that the inclusion of virtual nodes significantly enhances long-term prediction accuracy while also improving layer-wise sensitivity to mitigate the over-squashing problem. Virtual nodes also offer enhanced explainability by focusing on key intersections and high-traffic areas, as shown by the visualization of their adjacency matrix weights on road network heat maps. Our advanced approach enhances the understanding and management of urban traffic systems, making it particularly well-suited for real-world applications.
Paper Structure (18 sections, 11 equations, 8 figures, 2 tables)

This paper contains 18 sections, 11 equations, 8 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Problem description and preliminaries
  3. Graph neural networks
  4. ST-GNNs for traffic prediction
  5. Long-term traffic prediction
  6. Literature Review
  7. Traffic prediction with ST-GNN
  8. Graph rewiring
  9. Methodology
  10. Framework of STGCN
  11. Semi-adaptive adjacency matrix with virtual nodes
  12. Experiment
  13. Dataset
  14. Baseline models and evaluation metrics
  15. Model comparison
  16. ...and 3 more sections

Figures (8)

  • Figure 1: GNN with Virtual Node Augmentation
  • Figure 1: Detailed Characteristics of the SD Dataset. B: billion ($10^9$)
  • Figure 2: Traffic Prediction Framework Incorporating Virtual Nodes
  • Figure 3: Visualization of Sensor Locations in San Diego
  • Figure 4: Adjacency Matrix Heat Map
  • ...and 3 more figures