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

TL;DR

This paper introduces a new tensor decomposition method that automatically determines the rank, avoids iterative procedures, and improves accuracy and efficiency for high-dimensional tensor data analysis.

Contribution

It presents a non-iterative tensor low-rank approximation technique using statistical thresholding, eliminating the need for predefined ranks and reducing computational costs.

Findings

Outperforms HOSVD, HOOI, and Tucker-L2E in accuracy

Reduces noise while preserving structure

Offers a fully automatic, theoretically grounded approach

Abstract

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.