# Truncated tensor Schatten p-norm based approach for spatiotemporal traffic data imputation with complicated missing patterns

arXiv: https://arxiv.org/abs/2205.09390 · HTML: https://mlsanity.com/paper/2205.09390/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 74 references that are in the map.
- First posted on arXiv 19 May 2022.

## Builds on (most cited first, 11 of 11)

- [Global Convergence of ADMM in Nonconvex Nonsmooth Optimization](https://mlsanity.com/paper/1511.06324/) (2015)
- [Bayesian Temporal Factorization for Multidimensional Time Series Prediction](https://mlsanity.com/paper/1910.06366/) (2019)
- [Low-Rank Autoregressive Tensor Completion for Spatiotemporal Traffic Data Imputation](https://mlsanity.com/paper/2104.14936/) (2021)
- [Weighted Schatten p-Norm Minimization for Image Denoising and Background Subtraction](https://mlsanity.com/paper/1512.01003/) (2015)
- [A Nonconvex Low-Rank Tensor Completion Model for Spatiotemporal Traffic Data Imputation](https://mlsanity.com/paper/2003.10271/) (2020)
- [Imputation and low-rank estimation with Missing Not At Random data](https://mlsanity.com/paper/1812.11409/) (2018)
- [Missing Slice Recovery for Tensors Using a Low-rank Model in Embedded Space](https://mlsanity.com/paper/1804.01736/) (2018)
- [Scalable Low-Rank Tensor Learning for Spatiotemporal Traffic Data Imputation](https://mlsanity.com/paper/2008.03194/) (2020)
- [Large-Scale Low-Rank Matrix Learning with Nonconvex Regularizers](https://mlsanity.com/paper/1708.00146/) (2017)
- [Multi-Output Gaussian Processes for Crowdsourced Traffic Data Imputation](https://mlsanity.com/paper/1812.08739/) (2018)
- [On the Efficiency of Random Permutation for ADMM and Coordinate Descent](https://mlsanity.com/paper/1503.06387/) (2015)

## Built on by (most cited first, 11 of 11)

- [ImputeFormer: Low Rankness-Induced Transformers for Generalizable Spatiotemporal Imputation](https://mlsanity.com/paper/2312.01728/) (2023)
- [Correlating sparse sensing for large-scale traffic speed estimation: A Laplacian-enhanced low-rank tensor kriging approach](https://mlsanity.com/paper/2210.11780/) (2022)
- [Towards better traffic volume estimation: Jointly addressing the underdetermination and nonequilibrium problems with correlation-adaptive GNNs](https://mlsanity.com/paper/2303.05660/) (2023)
- [Spatiotemporal Implicit Neural Representation as a Generalized Traffic Data Learner](https://mlsanity.com/paper/2405.03185/) (2024)
- [High-Dimensional Fault Tolerance Testing of Highly Automated Vehicles Based on Low-Rank Models](https://mlsanity.com/paper/2407.21069/) (2024)
- [A Parameter-free Nonconvex Low-rank Tensor Completion Model for Spatiotemporal Traffic Data Recovery](https://mlsanity.com/paper/2209.13786/) (2022)
- [Collaborative Imputation of Urban Time Series through Cross-city Meta-learning](https://mlsanity.com/paper/2501.11306/) (2025)
- [MNT-TNN: Spatiotemporal Traffic Data Imputation via Compact Multimode Nonlinear Transform-based Tensor Nuclear Norm](https://mlsanity.com/paper/2503.22955/) (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)

## Abstract (arXiv)

Rapid advances in sensor, wireless communication, cloud computing and data science have brought unprecedented amount of data to assist transportation engineers and researchers in making better decisions. However, traffic data in reality often has corrupted or incomplete values due to detector and communication malfunctions. Data imputation is thus required to ensure the effectiveness of downstream data-driven applications. To this end, numerous tensor-based methods treating the imputation problem as the low-rank tensor completion (LRTC) have been attempted in previous works. To tackle rank minimization, which is at the core of the LRTC, most of aforementioned methods utilize the tensor nuclear norm (NN) as a convex surrogate for the minimization. However, the over-relaxation issue in NN refrains it from desirable performance in practice. In this paper, we define an innovative nonconvex truncated Schatten p-norm for tensors (TSpN) to approximate tensor rank and impute missing spatiotemporal traffic data under the LRTC framework. We model traffic data into a third-order tensor structure of (time intervals,locations (sensors),days) and introduce four complicated missing patterns, including random missing and three fiber-like missing cases according to the tensor mode-n fibers. Despite nonconvexity of the objective function in our model, we derive the global optimal solutions by integrating the alternating direction method of multipliers (ADMM) with generalized soft-thresholding (GST). In addition, we design a truncation rate decay strategy to deal with varying missing rate scenarios. Comprehensive experiments are finally conducted using real-world spatiotemporal datasets, which demonstrate that the proposed LRTC-TSpN method performs well under various missing cases, meanwhile outperforming other SOTA tensor-based imputation models in almost all scenarios.