# A Nonconvex Low-Rank Tensor Completion Model for Spatiotemporal Traffic Data Imputation

arXiv: https://arxiv.org/abs/2003.10271 · HTML: https://mlsanity.com/paper/2003.10271/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Mar 2020.

## Built on by (most cited first, 27 of 27)

- [ImputeFormer: Low Rankness-Induced Transformers for Generalizable Spatiotemporal Imputation](https://mlsanity.com/paper/2312.01728/) (2023)
- [Low-Rank Autoregressive Tensor Completion for Spatiotemporal Traffic Data Imputation](https://mlsanity.com/paper/2104.14936/) (2021)
- [Low-Rank Hankel Tensor Completion for Traffic Speed Estimation](https://mlsanity.com/paper/2105.11335/) (2021)
- [Laplacian Convolutional Representation for Traffic Time Series Imputation](https://mlsanity.com/paper/2212.01529/) (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)
- [Expand and Compress: Exploring Tuning Principles for Continual Spatio-Temporal Graph Forecasting](https://mlsanity.com/paper/2410.12593/) (2024)
- [Modeling Heterogeneous Relations across Multiple Modes for Potential Crowd Flow Prediction](https://mlsanity.com/paper/2101.06954/) (2021)
- [Spatiotemporal Implicit Neural Representation as a Generalized Traffic Data Learner](https://mlsanity.com/paper/2405.03185/) (2024)
- [STAMImputer: Spatio-Temporal Attention MoE for Traffic Data Imputation](https://mlsanity.com/paper/2506.08054/) (2025)
- [Low-rank Tensor Learning with Nonconvex Overlapped Nuclear Norm Regularization](https://mlsanity.com/paper/2205.03059/) (2022)
- [A generalizable framework for low-rank tensor completion with numerical priors](https://mlsanity.com/paper/2302.05881/) (2023)
- [Spatio-Temporal Denoising Graph Autoencoders with Data Augmentation for Photovoltaic Timeseries Data Imputation](https://mlsanity.com/paper/2302.10860/) (2023)
- [Tensor Train Completion from Fiberwise Observations Along a Single Mode](https://mlsanity.com/paper/2509.18149/) (2025)
- [Learning Higher-Order Interactions from Incomplete Spatiotemporal Data with Mixtures of Hypergraph Laplacians](https://mlsanity.com/paper/2605.17316/) (2026)
- [Unsupervised Knowledge Adaptation for Passenger Demand Forecasting](https://mlsanity.com/paper/2206.04053/) (2022)
- [A Parameter-free Nonconvex Low-rank Tensor Completion Model for Spatiotemporal Traffic Data Recovery](https://mlsanity.com/paper/2209.13786/) (2022)
- [Large-Scale Traffic Data Imputation with Spatiotemporal Semantic Understanding](https://mlsanity.com/paper/2301.11691/) (2023)
- [Unsupervised Abnormal Stop Detection for Long Distance Coaches with Low-Frequency GPS](https://mlsanity.com/paper/2411.04422/) (2024)
- [MNT-TNN: Spatiotemporal Traffic Data Imputation via Compact Multimode Nonlinear Transform-based Tensor Nuclear Norm](https://mlsanity.com/paper/2503.22955/) (2025)
- [Geological Field Restoration through the Lens of Image Inpainting](https://mlsanity.com/paper/2506.04869/) (2025)
- [Robust Tensor Completion via Gradient Tensor Nulclear L1-L2 Norm for Traffic Data Recovery](https://mlsanity.com/paper/2506.22732/) (2025)
- [Tensor Completion via Monotone Inclusion: Generalized Low-Rank Priors Meet Deep Denoisers](https://mlsanity.com/paper/2510.12425/) (2025)
- [A Spatio-Temporal Online Robust Tensor Recovery Approach for Streaming Traffic Data Imputation](https://mlsanity.com/paper/2511.01267/) (2025)
- [Exact Recovery of Non-Random Missing Multidimensional Time Series via Temporal Isometric Delay-Embedding Transform](https://mlsanity.com/paper/2512.10191/) (2025)
- [SATORIS-N: Spectral Analysis based Traffic Observation Recovery via Informed Subspaces and Nuclear-norm minimization](https://mlsanity.com/paper/2602.03138/) (2026)
- [Low-rank Distributional Matrix Completion](https://mlsanity.com/paper/2606.04176/) (2026)

## Abstract (arXiv)

Sparsity and missing data problems are very common in spatiotemporal traffic data collected from various sensing systems. Making accurate imputation is critical to many applications in intelligent transportation systems. In this paper, we formulate the missing data imputation problem in spatiotemporal traffic data in a low-rank tensor completion (LRTC) framework and define a novel truncated nuclear norm (TNN) on traffic tensors of location×day×time of day. In particular, we introduce an universal rate parameter to control the degree of truncation on all tensor modes in the proposed LRTC-TNN model, and this allows us to better characterize the hidden patterns in spatiotemporal traffic data. Based on the framework of the Alternating Direction Method of Multipliers (ADMM), we present an efficient algorithm to obtain the optimal solution for each variable. We conduct numerical experiments on four spatiotemporal traffic data sets, and our results show that the proposed LRTC-TNN model outperforms many state-of-the-art imputation models with missing rates/patterns. Moreover, the proposed model also outperforms other baseline models in extreme missing scenarios.