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PAST: A Primary-Auxiliary Spatio-Temporal Network for Traffic Time Series Imputation

Hanwen Hu, Zimo Wen, Shiyou Qian, Jian Co

TL;DR

PAST tackles traffic time series imputation by disentangling internal primary patterns from external auxiliary patterns and coupling a Graph-Integrated Module (GIM) with a Cross-Gated Module (CGM). GIM learns primary patterns via dynamic directed graphs with interval-aware dropout and multi-order spatial propagation, while CGM extracts auxiliary patterns from external features through bidirectional gating, with their outputs combined in an ensemble self-supervised objective. Across METR-LA, PeMS-Bay, and LargeST-SD under 27 missing conditions, PAST consistently outperforms seven baselines, achieving up to 26.2% RMSE and 31.6% MAE improvements and demonstrating robustness to random, fiber, and block missing data. The work advances traffic-imputation methods by aligning pattern extraction with missing-type conditions, offering scalable and stable performance for real-world ITS applications.

Abstract

Traffic time series imputation is crucial for the safety and reliability of intelligent transportation systems, while diverse types of missing data, including random, fiber, and block missing make the imputation task challenging. Existing models often focus on disentangling and separately modeling spatial and temporal patterns based on relationships between data points. However, these approaches struggle to adapt to the random missing positions, and fail to learn long-term and large-scale dependencies, which are essential in extensive missing conditions. In this paper, patterns are categorized into two types to handle various missing data conditions: primary patterns, which originate from internal relationships between data points, and auxiliary patterns, influenced by external factors like timestamps and node attributes. Accordingly, we propose the Primary-Auxiliary Spatio-Temporal network (PAST). It comprises a graph-integrated module (GIM) and a cross-gated module (CGM). GIM captures primary patterns via dynamic graphs with interval-aware dropout and multi-order convolutions, and CGM extracts auxiliary patterns through bidirectional gating on embedded external features. The two modules interact via shared hidden vectors and are trained under an ensemble self-supervised framework. Experiments on three datasets under 27 missing data conditions demonstrate that the imputation accuracy of PAST outperforms seven state-of-the-art baselines by up to 26.2% in RMSE and 31.6% in MAE.

PAST: A Primary-Auxiliary Spatio-Temporal Network for Traffic Time Series Imputation

TL;DR

PAST tackles traffic time series imputation by disentangling internal primary patterns from external auxiliary patterns and coupling a Graph-Integrated Module (GIM) with a Cross-Gated Module (CGM). GIM learns primary patterns via dynamic directed graphs with interval-aware dropout and multi-order spatial propagation, while CGM extracts auxiliary patterns from external features through bidirectional gating, with their outputs combined in an ensemble self-supervised objective. Across METR-LA, PeMS-Bay, and LargeST-SD under 27 missing conditions, PAST consistently outperforms seven baselines, achieving up to 26.2% RMSE and 31.6% MAE improvements and demonstrating robustness to random, fiber, and block missing data. The work advances traffic-imputation methods by aligning pattern extraction with missing-type conditions, offering scalable and stable performance for real-world ITS applications.

Abstract

Traffic time series imputation is crucial for the safety and reliability of intelligent transportation systems, while diverse types of missing data, including random, fiber, and block missing make the imputation task challenging. Existing models often focus on disentangling and separately modeling spatial and temporal patterns based on relationships between data points. However, these approaches struggle to adapt to the random missing positions, and fail to learn long-term and large-scale dependencies, which are essential in extensive missing conditions. In this paper, patterns are categorized into two types to handle various missing data conditions: primary patterns, which originate from internal relationships between data points, and auxiliary patterns, influenced by external factors like timestamps and node attributes. Accordingly, we propose the Primary-Auxiliary Spatio-Temporal network (PAST). It comprises a graph-integrated module (GIM) and a cross-gated module (CGM). GIM captures primary patterns via dynamic graphs with interval-aware dropout and multi-order convolutions, and CGM extracts auxiliary patterns through bidirectional gating on embedded external features. The two modules interact via shared hidden vectors and are trained under an ensemble self-supervised framework. Experiments on three datasets under 27 missing data conditions demonstrate that the imputation accuracy of PAST outperforms seven state-of-the-art baselines by up to 26.2% in RMSE and 31.6% in MAE.

Paper Structure

This paper contains 42 sections, 12 equations, 6 figures, 10 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. General Time Series Imputation Models
  4. Traffic-Specific Imputation Models
  5. External Information for Time Series
  6. Summary
  7. Preliminaries
  8. Methodology
  9. Basic Ideas
  10. Graph-Integrated Module
  11. Temporal Layer
  12. Temporal Graph Building.
  13. Interval-aware Dropout.
  14. External Info Injection.
  15. Feed Forward Process
  16. ...and 27 more sections

Figures (6)

  • Figure 1: Three types of missing data in traffic scenarios.
  • Figure 2: The time series record the speed of a node in the PeMS-Bay dataset dcrnn. It provides specific examples of random and fiber missing.
  • Figure 3: The framework of PAST.
  • Figure 4: Graph-integrated layer for primary patterns
  • Figure 5: Cross-gated layer for auxiliary patterns
  • ...and 1 more figures