mlsanityData to 14 Oct 2026

Low-Rank Hankel Tensor Completion for Traffic Speed Estimation

arXiv 2105.11335 ↗First posted 21 May 2021cs.LG eess.SPcited by 22

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Abstract (arXiv)

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.

Key facts. Cited by 22 papers in the map (data through 14 Oct 2026). Builds on 10 of its 42 references that are in the map. First posted on arXiv 21 May 2021.

Builds on

10 of 42 references.

References · 10

  1. 2018Tensor Robust Principal Component Analysis with A New Tensor Nuclear Normcited by 112
  2. 2020Inductive Graph Neural Networks for Spatiotemporal Krigingcited by 91
  3. 2015Exact tensor completion using t-SVDcited by 70
  4. 2013Square Deal: Lower Bounds and Improved Relaxations for Tensor Recoverycited by 37
  5. 2020A Nonconvex Low-Rank Tensor Completion Model for Spatiotemporal Traffic Data Imputationcited by 27
  6. 2020Macroscopic Traffic Flow Modeling with Physics Regularized Gaussian Process: A New Insight into Machine Learning Applicationscited by 25
  7. 2018Missing Slice Recovery for Tensors Using a Low-rank Model in Embedded Spacecited by 17
  8. 2020Block Hankel Tensor ARIMA for Multiple Short Time Series Forecastingcited by 12
  9. 2021Incorporating Kinematic Wave Theory into a Deep Learning Method for High-Resolution Traffic Speed Estimationcited by 12
  10. 2017Large-Scale Low-Rank Matrix Learning with Nonconvex Regularizerscited by 10

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 2; 2022: 3; 2023: 7; 2024: 3; 2025: 5; 2026: 2.

22 papers.

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  1. 2023ImputeFormer: Low Rankness-Induced Transformers for Generalizable Spatiotemporal Imputationcited by 50
  2. 2021A Physics-Informed Deep Learning Paradigm for Traffic State and Fundamental Diagram Estimationcited by 37
  3. 2022Uncertainty Quantification of Sparse Travel Demand Prediction with Spatial-Temporal Graph Neural Networkscited by 29
  4. 2023Uncertainty Quantification via Spatial-Temporal Tweedie Model for Zero-inflated and Long-tail Travel Demand Predictioncited by 19
  5. 2022Laplacian Convolutional Representation for Traffic Time Series Imputationcited by 18
  6. 2022Correlating sparse sensing for large-scale traffic speed estimation: A Laplacian-enhanced low-rank tensor kriging approachcited by 17
  7. 2023ST-GIN: An Uncertainty Quantification Approach in Traffic Data Imputation with Spatio-temporal Graph Attention and Bidirectional Recurrent United Neural Networkscited by 8
  8. 2024Spatiotemporal Implicit Neural Representation as a Generalized Traffic Data Learnercited by 7
  9. 2023Traffic State Estimation from Vehicle Trajectories with Anisotropic Gaussian Processescited by 6
  10. 2021Hankel-structured Tensor Robust PCA for Multivariate Traffic Time Series Anomaly Detectioncited by 4
  11. 2023Fairness-Enhancing Vehicle Rebalancing in the Ride-hailing Systemcited by 3
  12. 2024Knowledge-data fusion oriented traffic state estimation: A stochastic physics-informed deep learning approachcited by 3
10 more
  1. 2023Spatiotemporal Regularized Tucker Decomposition Approach for Traffic Data Imputationcited by 2
  2. 2024Efficient and Robust Freeway Traffic Speed Estimation under Oblique Grid using Vehicle Trajectory Datacited by 2
  3. 2025Guaranteed Multidimensional Time Series Prediction via Deterministic Tensor Completion Theorycited by 2
  4. 2025PMA-Diffusion: A Physics-guided Mask-Aware Diffusion Framework for TSE from Sparse Observationscited by 1
  5. 2023Structured Low-Rank Tensor Learningcited by 0
  6. 2025Collaborative Imputation of Urban Time Series through Cross-city Meta-learningcited by 0
  7. 2025Robust Tensor Completion via Gradient Tensor Nulclear L1-L2 Norm for Traffic Data Recoverycited by 0
  8. 2025Exact Recovery of Non-Random Missing Multidimensional Time Series via Temporal Isometric Delay-Embedding Transformcited by 0
  9. 2026Uncertainty-Aware Graph Neural Reconstruction of Urban Temperature Fields from Sparse Sensors under Deployment Constraintscited by 0
  10. 2026Dual-Attention Convolution Experts for Sparse Tensor Completioncited by 0