无需预设秩和迭代，自动提取显著成分并降噪。
A Robust and Non-Iterative Tensor Decomposition Method with Automatic Thresholding
- 基于奇异值硬阈值法，按模式展开矩阵自动筛选重要成分
- 在模拟实验中精度和效率均优于HOSVD、HOOI和Tucker-L2E
- 适合缺乏先验知识或追求高效处理高维张量数据的场景
物联网与生物传感技术的发展催生了海量高维张量数据，但实现精确高效的低秩逼近仍面临挑战。现有张量分解方法通常需预先设定秩并依赖迭代优化，导致计算成本高且依赖人工经验。本文提出一种新型张量低秩逼近方法，无需预设秩也无需迭代优化。该方法对每种模式展开的矩阵应用统计奇异值硬阈值，自动提取具有统计显著性的成分，有效抑制噪声同时保留内在结构。理论上，各模式的最优阈值由Marcenko-Pastur分布的渐近性质导出。模拟实验表明，所提方法在估计精度和计算效率上均优于传统方法（HOSVD、HOOI 和 Tucker-L2E）。结果表明，该方法提供了一个理论严谨、完全自动、非迭代的张量分解框架。
原文摘要 · Abstract (English)
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.
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