# Spatiotemporal Regularized Tucker Decomposition Approach for Traffic Data Imputation

arXiv: https://arxiv.org/abs/2305.06563 · HTML: https://mlsanity.com/paper/2305.06563/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 46 references that are in the map.
- First posted on arXiv 11 May 2023.

## Builds on (most cited first, 15 of 15)

- [Exact tensor completion using t-SVD](https://mlsanity.com/paper/1502.04689/) (2015)
- [Tensor Completion Algorithms in Big Data Analytics](https://mlsanity.com/paper/1711.10105/) (2017)
- [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)
- [Low-Rank Hankel Tensor Completion for Traffic Speed Estimation](https://mlsanity.com/paper/2105.11335/) (2021)
- [Efficient Nonnegative Tucker Decompositions: Algorithms and Uniqueness](https://mlsanity.com/paper/1404.4412/) (2014)
- [Missing Slice Recovery for Tensors Using a Low-rank Model in Embedded Space](https://mlsanity.com/paper/1804.01736/) (2018)
- [Block Hankel Tensor ARIMA for Multiple Short Time Series Forecasting](https://mlsanity.com/paper/2002.12135/) (2020)
- [Scalable Low-Rank Tensor Learning for Spatiotemporal Traffic Data Imputation](https://mlsanity.com/paper/2008.03194/) (2020)
- [Alternating proximal gradient method for sparse nonnegative Tucker decomposition](https://mlsanity.com/paper/1302.2559/) (2013)
- [Spatiotemporal Tensor Completion for Improved Urban Traffic Imputation](https://mlsanity.com/paper/2103.08323/) (2021)
- [Understanding Urban Dynamics via Context-aware Tensor Factorization with Neighboring Regularization](https://mlsanity.com/paper/1905.00702/) (2019)
- [Discovering Dynamic Patterns from Spatiotemporal Data with Time-Varying Low-Rank Autoregression](https://mlsanity.com/paper/2211.15482/) (2022)
- [Improving "Fast Iterative Shrinkage-Thresholding Algorithm": Faster, Smarter and Greedier](https://mlsanity.com/paper/1811.01430/) (2018)
- [Low-Rank and Sparse Enhanced Tucker Decomposition for Tensor Completion](https://mlsanity.com/paper/2010.00359/) (2020)

## Built on by (most cited first, 2 of 2)

- [LRTuckerRep: Low-rank Tucker Representation Model for Multi-dimensional Data Completion](https://mlsanity.com/paper/2508.03755/) (2025)
- [A Spatio-Temporal Online Robust Tensor Recovery Approach for Streaming Traffic Data Imputation](https://mlsanity.com/paper/2511.01267/) (2025)

## Abstract (arXiv)

In intelligent transportation systems, traffic data imputation, estimating the missing value from partially observed data is an inevitable and challenging task. Previous studies have not fully considered traffic data's multidimensionality and spatiotemporal correlations, but they are vital to traffic data recovery, especially for high-level missing scenarios. To address this problem, we propose a novel spatiotemporal regularized Tucker decomposition method. First, the traffic matrix is converted into a third-order tensor. Then, based on Tucker decomposition, the tensor is approximated by multiplying non-negative factor matrices with a sparse core tensor. Notably, we do not need to set the tensor rank or determine it through matrix nuclear-norm minimization or tensor rank minimization. The low rankness is characterized by the l1-norm of the core tensor, while the manifold regularization and temporal constraint are employed to capture spatiotemporal correlations and further improve imputation performance. We use an alternating proximal gradient method with guaranteed convergence to address the proposed model. Numerical experiments show that our proposal outperforms matrix-based and tensor-based baselines on real-world spatiotemporal traffic datasets in various missing scenarios.