# A Robust and Non-Iterative Tensor Decomposition Method with Automatic Thresholding

arXiv: https://arxiv.org/abs/2505.06203 · HTML: https://mlsanity.com/paper/2505.06203/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 43 references that are in the map.
- First posted on arXiv 9 May 2025.

## Builds on (most cited first, 9 of 9)

- [Exact tensor completion using t-SVD](https://mlsanity.com/paper/1502.04689/) (2015)
- [Tensor SVD: Statistical and Computational Limits](https://mlsanity.com/paper/1703.02724/) (2017)
- [Robust Low-rank Tensor Recovery: Models and Algorithms](https://mlsanity.com/paper/1311.6182/) (2013)
- [Bayesian Robust Tensor Factorization for Incomplete Multiway Data](https://mlsanity.com/paper/1410.2386/) (2014)
- [Optimal High-order Tensor SVD via Tensor-Train Orthogonal Iteration](https://mlsanity.com/paper/2010.02482/) (2020)
- [Graph Regularized Tensor Train Decomposition](https://mlsanity.com/paper/1911.01591/) (2019)
- [Robust Low-rank Tensor Decomposition with the operatornameL2 Criterion](https://mlsanity.com/paper/2208.11806/) (2022)
- [Tensor-Train Parameterization for Ultra Dimensionality Reduction](https://mlsanity.com/paper/1908.04924/) (2019)
- [Tensor Methods in High Dimensional Data Analysis: Opportunities and Challenges](https://mlsanity.com/paper/2405.18412/) (2024)

## Abstract (arXiv)

Recent advances in IoT and biometric sensing technologies have led to the generation of massive and high-dimensional tensor data, yet achieving accurate and efficient low-rank approximation remains a major challenge. Most existing tensor decomposition methods require predefined ranks and iterative optimization, resulting in high computational costs and dependence on analyst expertise. This study proposes a novel tensor low-rank approximation method that eliminates both prior rank specification and iterative optimization. The method applies statistical singular value hard thresholding to each mode-wise unfolded matrix to automatically extract statistically significant components, effectively reducing noise while preserving the intrinsic structure. Theoretically, the optimal thresholds for each mode are derived from the asymptotic properties of the Marcenko-Pastur distribution. Simulation experiments demonstrate that the proposed method outperforms conventional approaches (HOSVD, HOOI, and Tucker-L2E) in both estimation accuracy and computational efficiency. These results indicate that the proposed approach provides a theoretically grounded, fully automatic, and non-iterative framework for tensor decomposition.