Low-Rank Hankel Tensor Completion for Traffic Speed Estimation

Abstract

This paper studies the traffic state estimation (TSE) problem using sparse observations from mobile sensors. Most existing TSE methods either rely on well-defined physical traffic flow models or require large amounts of simulation data as input to train machine learning models. Different from previous studies, we propose a purely data-driven and model-free solution in this paper. We consider the TSE as a spatiotemporal matrix completion/interpolation problem, and apply spatiotemporal delay embedding to transform the original incomplete matrix into a fourth-order Hankel structured tensor. By imposing a low-rank assumption on this tensor structure, we can approximate and characterize both global and local spatiotemporal patterns in a data-driven manner. We use the truncated nuclear norm of a balanced spatiotemporal unfolding -- in which each column represents the vectorization of a small patch in the original matrix -- to approximate the tensor rank. An efficient solution algorithm based on the Alternating Direction Method of Multipliers (ADMM) is developed for model learning. The proposed framework only involves two hyperparameters, spatial and temporal window lengths, which are easy to set given the degree of data sparsity. We conduct numerical experiments on real-world high-resolution trajectory data, and our results demonstrate the effectiveness and superiority of the proposed model in some challenging scenarios.

References in corpus (6)

• Linearized Alternating Direction Method with Adaptive Penalty for Low-Rank Representation
• Square Deal: Lower Bounds and Improved Relaxations for Tensor Recovery
• A Nonconvex Low-Rank Tensor Completion Model for Spatiotemporal Traffic Data Imputation
• Macroscopic Traffic Flow Modeling with Physics Regularized Gaussian Process: A New Insight into Machine Learning Applications
• Inductive Graph Neural Networks for Spatiotemporal Kriging
• Incorporating Kinematic Wave Theory into a Deep Learning Method for High-Resolution Traffic Speed Estimation

Cited by in corpus (2)

• Correlating sparse sensing for large-scale traffic speed estimation: A Laplacian-enhanced low-rank tensor kriging approach
• Hankel-structured Tensor Robust PCA for Multivariate Traffic Time Series Anomaly Detection