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Traffic Flow Data Completion and Anomaly Diagnosis via Sparse and Low-Rank Tensor Optimization

Junxi Man, Yumin Lin, Xiaoyu Li

TL;DR

Traffic data are often incomplete and contaminated, hindering reliable completion and anomaly detection. The authors propose TSLTO, a Tucker-based sparse-low-rank high-order tensor optimization model that separates data into a global low-rank component and a block-sparse anomaly tensor, with Toeplitz-based locality constraints, solved via an ADMM algorithm. The approach yields higher accuracy and efficiency than existing methods on synthetic data and the Guangzhou city traffic speed dataset, with ablation studies confirming the value of each regularization term. This work advances traffic data analytics by exploiting spatiotemporal correlations and local continuity to achieve robust imputation and precise anomaly diagnosis, with potential extensions to speed prediction and distributed optimization.

Abstract

Spatiotemporal traffic time series, such as traffic speed data, collected from sensing systems are often incomplete, with considerable corruption and large amounts of missing values. A vast amount of data conceals implicit data structures, which poses significant challenges for data recovery issues, such as mining the potential spatio-temporal correlations of data and identifying abnormal data. In this paper, we propose a Tucker decomposition-based sparse low-rank high-order tensor optimization model (TSLTO) for data imputation and anomaly diagnosis. We decompose the traffic tensor data into low-rank and sparse tensors, and establish a sparse low-rank high-order tensor optimization model based on Tucker decomposition. By utilizing tools of non-smooth analysis for tensor functions, we explore the optimality conditions of the proposed tensor optimization model and design an ADMM optimization algorithm for solving the model. Finally, numerical experiments are conducted on both synthetic data and a real-world dataset: the urban traffic speed dataset of Guangzhou. Numerical comparisons with several representative existing algorithms demonstrate that our proposed approach achieves higher accuracy and efficiency in traffic flow data recovery and anomaly diagnosis tasks.

Traffic Flow Data Completion and Anomaly Diagnosis via Sparse and Low-Rank Tensor Optimization

TL;DR

Traffic data are often incomplete and contaminated, hindering reliable completion and anomaly detection. The authors propose TSLTO, a Tucker-based sparse-low-rank high-order tensor optimization model that separates data into a global low-rank component and a block-sparse anomaly tensor, with Toeplitz-based locality constraints, solved via an ADMM algorithm. The approach yields higher accuracy and efficiency than existing methods on synthetic data and the Guangzhou city traffic speed dataset, with ablation studies confirming the value of each regularization term. This work advances traffic data analytics by exploiting spatiotemporal correlations and local continuity to achieve robust imputation and precise anomaly diagnosis, with potential extensions to speed prediction and distributed optimization.

Abstract

Spatiotemporal traffic time series, such as traffic speed data, collected from sensing systems are often incomplete, with considerable corruption and large amounts of missing values. A vast amount of data conceals implicit data structures, which poses significant challenges for data recovery issues, such as mining the potential spatio-temporal correlations of data and identifying abnormal data. In this paper, we propose a Tucker decomposition-based sparse low-rank high-order tensor optimization model (TSLTO) for data imputation and anomaly diagnosis. We decompose the traffic tensor data into low-rank and sparse tensors, and establish a sparse low-rank high-order tensor optimization model based on Tucker decomposition. By utilizing tools of non-smooth analysis for tensor functions, we explore the optimality conditions of the proposed tensor optimization model and design an ADMM optimization algorithm for solving the model. Finally, numerical experiments are conducted on both synthetic data and a real-world dataset: the urban traffic speed dataset of Guangzhou. Numerical comparisons with several representative existing algorithms demonstrate that our proposed approach achieves higher accuracy and efficiency in traffic flow data recovery and anomaly diagnosis tasks.

Paper Structure

This paper contains 17 sections, 39 equations, 6 figures, 4 tables, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. PRELIMINARIES
  3. Notations
  4. Tensor Basics
  5. OPTIMIZATION APPROACH
  6. TSLTO
  7. ADMM
  8. NUMERICAL EXPERIMENTS
  9. Evaluation Criteria
  10. Dataset Description
  11. Synthetic Dataset
  12. Real-world Datasets
  13. Parameter Tuning and Evaluation Results
  14. Ablation Study
  15. Sensitivity Analysis
  16. ...and 2 more sections

Figures (6)

  • Figure 1: Application of Tucker decomposition in real traffic dataset. On the left side, from left to right: raw data, low-rank structure, sparse structure; on the right side: compression ratio.
  • Figure 2: Core tensor and factor matrices generated by Tucker decomposition
  • Figure 3: Synthetic data slice. Subfigure (a) displays the original synthetic tensor, subfigure (b) visualizes the low-rank component, and subfigure (c) highlights the sparse anomaly component.
  • Figure 4: Data imputation and anomaly diagnosis performance under varying missing rates. Each row demonstrates results at 10%, 20%, 30%, and 40% missing rates respectively. Subfigure (a) shows the low-rank component of the original tensor slice, (b) displays the sparse anomaly component, (c) presents the complete original slice, (d) depicts the observed incomplete slice, (e) visualizes the recovered low-rank slice, and (f) identifies the detected block-sparse anomaly slice. All slices represent the 12th frontal slice along the third mode of the tensor.
  • Figure 5: Grid Search Results of $\beta$ and $\lambda$
  • ...and 1 more figures