Low-Rank Hankel Tensor Completion for Traffic Speed Estimation

• URL: http://arxiv.org/abs/2105.11335v1
• Date: Fri, 21 May 2021 00:08:06 GMT
• Title: Low-Rank Hankel Tensor Completion for Traffic Speed Estimation
• Authors: Xudong Wang, Yuankai Wu, Dingyi Zhuang, Lijun Sun
• Abstract summary: We propose a purely data-driven and model-free solution to the traffic state estimation problem. By imposing a low-rank assumption on this tensor structure, we can approximate characterize both global patterns and the unknown complex local dynamics. We conduct numerical experiments on both synthetic simulation data and real-world high-resolution data, and our results demonstrate the effectiveness and superiority of the proposed model.
• Score: 7.346671461427793
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper studies the traffic state estimation (TSE) problem using sparse observations from mobile sensors. TSE can be considered a spatiotemporal interpolation problem in which the evolution of traffic variables (e.g., speed/density) is governed by traffic flow dynamics (e.g., partial differential equations). 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, in this paper we propose a purely data-driven and model-free solution. We consider TSE as a spatiotemporal matrix completion/interpolation problem, and apply spatiotemporal Hankel delay embedding to transforms the original incomplete matrix to a fourth-order tensor. By imposing a low-rank assumption on this tensor structure, we can approximate and characterize both global patterns and the unknown and complex local spatiotemporal dynamics in a data-driven manner. We use the truncated nuclear norm of the spatiotemporal unfolding (i.e., square norm) to approximate the tensor rank and develop an efficient solution algorithm based on the Alternating Direction Method of Multipliers (ADMM). 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 both synthetic simulation data and real-world high-resolution trajectory data, and our results demonstrate the effectiveness and superiority of the proposed model in some challenging scenarios.

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