# Low-Rank Autoregressive Tensor Completion for Spatiotemporal Traffic Data Imputation

arXiv: https://arxiv.org/abs/2104.14936 · HTML: https://mlsanity.com/paper/2104.14936/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 20 references that are in the map.
- First posted on arXiv 30 Apr 2021.

## Builds on (most cited first, 6 of 6)

- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Think Globally, Act Locally: A Deep Neural Network Approach to High-Dimensional Time Series Forecasting](https://mlsanity.com/paper/1905.03806/) (2019)
- [Bayesian Temporal Factorization for Multidimensional Time Series Prediction](https://mlsanity.com/paper/1910.06366/) (2019)
- [Smooth PARAFAC Decomposition for Tensor Completion](https://mlsanity.com/paper/1505.06611/) (2015)
- [Tensor Completion for Weakly-dependent Data on Graph for Metro Passenger Flow Prediction](https://mlsanity.com/paper/1912.05693/) (2019)
- [A Nonconvex Low-Rank Tensor Completion Model for Spatiotemporal Traffic Data Imputation](https://mlsanity.com/paper/2003.10271/) (2020)

## Built on by (most cited first, 30 of 35)

- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [ImputeFormer: Low Rankness-Induced Transformers for Generalizable Spatiotemporal Imputation](https://mlsanity.com/paper/2312.01728/) (2023)
- [Laplacian Convolutional Representation for Traffic Time Series Imputation](https://mlsanity.com/paper/2212.01529/) (2022)
- [Correlating sparse sensing for large-scale traffic speed estimation: A Laplacian-enhanced low-rank tensor kriging approach](https://mlsanity.com/paper/2210.11780/) (2022)
- [Truncated tensor Schatten p-norm based approach for spatiotemporal traffic data imputation with complicated missing patterns](https://mlsanity.com/paper/2205.09390/) (2022)
- [Physics-Informed Deep Learning For Traffic State Estimation: A Survey and the Outlook](https://mlsanity.com/paper/2303.02063/) (2023)
- [STD-PLM: Understanding Both Spatial and Temporal Properties of Spatial-Temporal Data with PLM](https://mlsanity.com/paper/2407.09096/) (2024)
- [Expand and Compress: Exploring Tuning Principles for Continual Spatio-Temporal Graph Forecasting](https://mlsanity.com/paper/2410.12593/) (2024)
- [ST-GIN: An Uncertainty Quantification Approach in Traffic Data Imputation with Spatio-temporal Graph Attention and Bidirectional Recurrent United Neural Networks](https://mlsanity.com/paper/2305.06480/) (2023)
- [Spatiotemporal Implicit Neural Representation as a Generalized Traffic Data Learner](https://mlsanity.com/paper/2405.03185/) (2024)
- [Improving the generalizability and robustness of large-scale traffic signal control](https://mlsanity.com/paper/2306.01925/) (2023)
- [Hankel-structured Tensor Robust PCA for Multivariate Traffic Time Series Anomaly Detection](https://mlsanity.com/paper/2110.04352/) (2021)
- [FastSTI: A Fast Conditional Pseudo Numerical Diffusion Model for Spatio-temporal Traffic Data Imputation](https://mlsanity.com/paper/2410.15248/) (2024)
- [Knowledge-data fusion oriented traffic state estimation: A stochastic physics-informed deep learning approach](https://mlsanity.com/paper/2409.00644/) (2024)
- [Spatiotemporal Regularized Tucker Decomposition Approach for Traffic Data Imputation](https://mlsanity.com/paper/2305.06563/) (2023)
- [Machine Learning for Missing Value Imputation](https://mlsanity.com/paper/2410.08308/) (2024)
- [STAMImputer: Spatio-Temporal Attention MoE for Traffic Data Imputation](https://mlsanity.com/paper/2506.08054/) (2025)
- [Generalized Least Squares Kernelized Tensor Factorization](https://mlsanity.com/paper/2412.07041/) (2024)
- [ZTFed-MAS2S: A Zero-Trust Federated Learning Framework with Verifiable Privacy and Trust-Aware Aggregation for Wind Power Data Imputation](https://mlsanity.com/paper/2508.18318/) (2025)
- [Learning Higher-Order Interactions from Incomplete Spatiotemporal Data with Mixtures of Hypergraph Laplacians](https://mlsanity.com/paper/2605.17316/) (2026)
- [A Parameter-free Nonconvex Low-rank Tensor Completion Model for Spatiotemporal Traffic Data Recovery](https://mlsanity.com/paper/2209.13786/) (2022)
- [Adaptive Anomaly Detection in Network Flows with Low-Rank Tensor Decompositions and Deep Unrolling](https://mlsanity.com/paper/2409.11529/) (2024)
- [A Survey and Benchmarking of Spatial-Temporal Traffic Data Imputation Models](https://mlsanity.com/paper/2412.04733/) (2024)
- [Effective and Efficient Cross-City Traffic Knowledge Transfer: A Privacy-Preserving Perspective](https://mlsanity.com/paper/2503.11963/) (2025)
- [MNT-TNN: Spatiotemporal Traffic Data Imputation via Compact Multimode Nonlinear Transform-based Tensor Nuclear Norm](https://mlsanity.com/paper/2503.22955/) (2025)
- [Kernel Dynamic Mode Decomposition For Sparse Reconstruction of Closable Koopman Operators](https://mlsanity.com/paper/2505.06806/) (2025)
- [Latent Factorization of Tensors with Threshold Distance Weighted Loss for Traffic Data Estimation](https://mlsanity.com/paper/2506.22441/) (2025)
- [Robust Tensor Completion via Gradient Tensor Nulclear L1-L2 Norm for Traffic Data Recovery](https://mlsanity.com/paper/2506.22732/) (2025)
- [LRTuckerRep: Low-rank Tucker Representation Model for Multi-dimensional Data Completion](https://mlsanity.com/paper/2508.03755/) (2025)
- [Tensor Completion via Monotone Inclusion: Generalized Low-Rank Priors Meet Deep Denoisers](https://mlsanity.com/paper/2510.12425/) (2025)

## Abstract (arXiv)

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 textittemporal variation as a new regularization term into the completion of a third-order (sensor × time of day × 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.