Auto Tensor Singular Value Thresholding: A Non-Iterative and Rank-Free Framework for Tensor Denoising

In modern data-driven tasks such as classification, optimization, and forecasting, mitigating the effects of intrinsic noise is crucial for improving predictive accuracy. While numerous denoising techniques have been developed, the rising dimensionality of real-world datasets limits conventional matrix-based methods in preserving data structure and accuracy. This challenge has led to increasing interest in tensor-based approaches, which naturally capture multi-way data relationships. However, classical tensor decomposition methods (e.g., HOSVD, HOOI) typically require pre-specified ranks and iterative optimization, making them computationally expensive and less practical. In this work, we propose a novel low-rank approximation method for tensor data that avoids these limitations. Our approach applies statistically grounded singular value thresholding to mode-wise matricizations, enabling automatic extraction of significant components without requiring prior rank specification or iterative refinement. Experiments on synthetic and real-world tensors show that our method consistently outperforms existing techniques in terms of estimation accuracy and computational efficiency, especially in noisy high-dimensional settings.