# MNT-TNN: Spatiotemporal Traffic Data Imputation via Compact Multimode Nonlinear Transform-based Tensor Nuclear Norm

arXiv: https://arxiv.org/abs/2503.22955 · HTML: https://mlsanity.com/paper/2503.22955/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 58 references that are in the map.
- First posted on arXiv 29 Mar 2025.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [GMAN: A Graph Multi-Attention Network for Traffic Prediction](https://mlsanity.com/paper/1911.08415/) (2019)
- [SCINet: Time Series Modeling and Forecasting with Sample Convolution and Interaction](https://mlsanity.com/paper/2106.09305/) (2021)
- [Tensor Robust Principal Component Analysis with A New Tensor Nuclear Norm](https://mlsanity.com/paper/1804.03728/) (2018)
- [Exact tensor completion using t-SVD](https://mlsanity.com/paper/1502.04689/) (2015)
- [Novel methods for multilinear data completion and de-noising based on tensor-SVD](https://mlsanity.com/paper/1407.1785/) (2014)
- [ImputeFormer: Low Rankness-Induced Transformers for Generalizable Spatiotemporal Imputation](https://mlsanity.com/paper/2312.01728/) (2023)
- [Framelet Representation of Tensor Nuclear Norm for Third-Order Tensor Completion](https://mlsanity.com/paper/1909.06982/) (2019)
- [Low-Rank Autoregressive Tensor Completion for Spatiotemporal Traffic Data Imputation](https://mlsanity.com/paper/2104.14936/) (2021)
- [Smooth PARAFAC Decomposition for Tensor Completion](https://mlsanity.com/paper/1505.06611/) (2015)
- [A Nonconvex Low-Rank Tensor Completion Model for Spatiotemporal Traffic Data Imputation](https://mlsanity.com/paper/2003.10271/) (2020)
- [Spatio-Temporal Graph Scattering Transform](https://mlsanity.com/paper/2012.03363/) (2020)
- [Correlating sparse sensing for large-scale traffic speed estimation: A Laplacian-enhanced low-rank tensor kriging approach](https://mlsanity.com/paper/2210.11780/) (2022)
- [Human-instructed Deep Hierarchical Generative Learning for Automated Urban Planning](https://mlsanity.com/paper/2212.00904/) (2022)
- [Nonlinear Transform Induced Tensor Nuclear Norm for Tensor Completion](https://mlsanity.com/paper/2110.08774/) (2021)
- [Scalable Low-Rank Tensor Learning for Spatiotemporal Traffic Data Imputation](https://mlsanity.com/paper/2008.03194/) (2020)
- [Truncated tensor Schatten p-norm based approach for spatiotemporal traffic data imputation with complicated missing patterns](https://mlsanity.com/paper/2205.09390/) (2022)
- [Robust Tensor Recovery with Fiber Outliers for Traffic Events](https://mlsanity.com/paper/1908.10198/) (2019)

## Abstract (arXiv)

Imputation of random or non-random missing data is a long-standing research topic and a crucial application for Intelligent Transportation Systems (ITS). However, with the advent of modern communication technologies such as Global Satellite Navigation Systems (GNSS), traffic data collection has introduced new challenges in random missing value imputation and increasing demands for spatiotemporal dependency modelings. To address these issues, we propose a novel spatiotemporal traffic imputation method based on a Multimode Nonlinear Transformed Tensor Nuclear Norm (MNT-TNN), which can effectively capture the intrinsic multimode spatiotemporal correlations and low-rankness of the traffic tensor, represented as location × location × time. To solve the nonconvex optimization problem, we design a proximal alternating minimization (PAM) algorithm with theoretical convergence guarantees. We also suggest an Augmented Transform-based Tensor Nuclear Norm Families (ATTNNs) framework to enhance the imputation results of TTNN techniques, especially at very high miss rates. Extensive experiments on real datasets demonstrate that our proposed MNT-TNN and ATTNNs can outperform the compared state-of-the-art imputation methods, completing the benchmark of random missing traffic value imputation.