[Paper Review] Low-Rank Autoregressive Tensor Completion for Spatiotemporal Traffic Data Imputation

Xinyu Chen, Mengying Lei+2 more|arXiv (Cornell University)|Apr 30, 2021

Tensor decomposition and applications28 references145 citations

TL;DR

This paper proposes Low-Rank Autoregressive Tensor Completion (LATC), a novel framework that integrates autoregressive modeling into low-rank tensor completion to improve spatiotemporal traffic data imputation. By modeling temporal dynamics via an AR(p) process and using truncated nuclear norm for low-rank approximation, LATC captures both global patterns (e.g., day-to-day similarity) and local temporal consistency, outperforming state-of-the-art methods across diverse missing data scenarios in real-world traffic datasets.

ABSTRACT

Spatiotemporal traffic time series (e.g., traffic volume/speed) collected from sensing systems are often incomplete with considerable corruption and large amounts of missing values, preventing users from harnessing the full power of the data. Missing data imputation has been a long-standing research topic and critical application for real-world intelligent transportation systems. A widely applied imputation method is low-rank matrix/tensor completion; however, the low-rank assumption only preserves the global structure while ignores the strong local consistency in spatiotemporal data. In this paper, we propose a low-rank autoregressive tensor completion (LATC) framework by introducing extit{temporal variation} as a new regularization term into the completion of a third-order (sensor $ imes$ time of day $ imes$ day) tensor. The third-order tensor structure allows us to better capture the global consistency of traffic data, such as the inherent seasonality and day-to-day similarity. To achieve local consistency, we design the temporal variation by imposing an AR($p$) model for each time series with coefficients as learnable parameters. Different from previous spatial and temporal regularization schemes, the minimization of temporal variation can better characterize temporal generative mechanisms beyond local smoothness, allowing us to deal with more challenging scenarios such "blackout" missing. To solve the optimization problem in LATC, we introduce an alternating minimization scheme that estimates the low-rank tensor and autoregressive coefficients iteratively. We conduct extensive numerical experiments on several real-world traffic data sets, and our results demonstrate the effectiveness of LATC in diverse missing scenarios.

Motivation & Objective

• To address the challenge of missing and corrupted spatiotemporal traffic data in intelligent transportation systems.
• To overcome the limitations of traditional low-rank matrix/tensor completion, which ignore local temporal consistency and generative dynamics.
• To develop a unified framework that models both global low-rank structure and local temporal dependencies in traffic time series.
• To enable accurate imputation under diverse missing data patterns, including random, non-random, and blackout missingness.
• To provide a robust, rank-free alternative to factorization-based models by using truncated nuclear norm and learnable autoregressive coefficients.

Proposed method

• Formulates spatiotemporal traffic data as a third-order tensor (sensor × time of day × day) to better capture day-to-day similarity and global structure.
• Uses truncated nuclear norm as a low-rank approximation to avoid the need for predefining a rank parameter.
• Introduces temporal variation as a regularization term based on an AR(p) model, where coefficients are learned from data to model temporal generative mechanisms.
• Constructs an objective function combining tensor low-rankness (via truncated nuclear norm) and temporal variation (sum of AR prediction errors).
• Employs an alternating minimization algorithm: ADMM for tensor update and closed-form least squares for autoregressive coefficient estimation.
• Unfolds the time series into a matrix and applies AR(p) modeling per sensor to enforce local temporal consistency beyond simple smoothness.

Experimental results

Research questions

• RQ1 Can integrating autoregressive modeling into low-rank tensor completion improve imputation accuracy for spatiotemporal traffic data?
• RQ2 How does the proposed LATC model perform under diverse missing data patterns, including random, non-random, and blackout missingness?
• RQ3 Does modeling temporal generative mechanisms (via AR(p)) lead to better imputation than relying solely on low-rank structure or local smoothness?
• RQ4 How does LATC compare to state-of-the-art matrix and tensor completion methods in terms of MAPE and RMSE across real-world traffic datasets?
• RQ5 Can the proposed framework be applied not only to imputation but also to forecasting under missing data conditions?

Key findings

• LATC achieves the lowest MAPE and RMSE across all missing data scenarios on four real-world traffic datasets, outperforming LAMC, LRTC-TNN, BTMF, and SPC.
• On the Hangzhou metro passenger flow dataset, LATC achieves 5.71% MAPE and 2.54 RMSE under 30% random missingness, outperforming LRTC-TNN (6.99/3.00) and BTMF (7.54/3.27).
• In the Seattle freeway speed dataset, LATC achieves 19.12% MAPE and 24.97 RMSE under 30% random missingness, significantly better than SPC (27.46/68.56) and BTMF (25.61/77.00).
• For the Portland traffic volume dataset with 30% blackout missingness (window length 4), LATC achieves 24.04% MAPE and 23.52 RMSE, outperforming SPC (31.01/60.33) and BTMF (27.85/25.68).
• LATC demonstrates robustness to high missing rates (up to 90%), maintaining lower error than all baselines, especially in non-random and blackout scenarios.
• Visualizations in Figs. 5–7 show that LATC accurately recovers true traffic patterns even with severe data loss, learning underlying temporal dynamics from sparse observations.