Optimal Sparse Singular Value Decomposition for High-dimensional High-order Data

• URL: http://arxiv.org/abs/1809.01796v2
• Date: Mon, 8 Jul 2024 02:19:52 GMT
• Title: Optimal Sparse Singular Value Decomposition for High-dimensional High-order Data
• Authors: Anru Zhang, Rungang Han,
• Abstract summary: We consider the sparse tensor singular value decomposition, which aims for reduction on high-dimensional high-order data with certain sparsity structure. A method named Sparse Alternating Thresholding for Singular Value Decomposition (STAT-SVD) is proposed. The proposed procedure features a novel double projection & thresholding scheme, which provides a sharp criterion for thresholding in each iteration.
• Score: 4.987670632802288
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: In this article, we consider the sparse tensor singular value decomposition, which aims for dimension reduction on high-dimensional high-order data with certain sparsity structure. A method named Sparse Tensor Alternating Thresholding for Singular Value Decomposition (STAT-SVD) is proposed. The proposed procedure features a novel double projection \& thresholding scheme, which provides a sharp criterion for thresholding in each iteration. Compared with regular tensor SVD model, STAT-SVD permits more robust estimation under weaker assumptions. Both the upper and lower bounds for estimation accuracy are developed. The proposed procedure is shown to be minimax rate-optimal in a general class of situations. Simulation studies show that STAT-SVD performs well under a variety of configurations. We also illustrate the merits of the proposed procedure on a longitudinal tensor dataset on European country mortality rates.

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