Low-CP-Rank Tensor Completion via Practical Regularization

作者：Jia-Hua Jiang, Fatoumata Sanogo, C. Navasca · 发表于：Journal of Scientific Computing · 年份：2021 · DOI：10.1007/s10915-022-01789-9 · 被引用次数：12 · 研究领域：Computer Science、Mathematics

Dimension reduction is analytical methods for reconstructing high-order tensors that the intrinsic rank of these tensor data is relatively much smaller than the dimension of the ambient measurement space. Typically, this is the case for most real world datasets in signals, images and machine learning. The CANDECOMP/PARAFAC (CP, aka Canonical Polyadic) tensor completion is a widely used approach to find a low-rank approximation for a given tensor. In the tensor model (Sanogo and Navasca in 2018 52nd Asilomar conference on signals, systems, and computers, pp 845–849, https://doi.org/10.1109/ACSSC.2018.8645405, 2018), a sparse regularization minimization problem via ℓ1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _1$$\end{document} norm was formulated with an appropriate choice of the regularization parameter. The choice of the regularization parameter is important in the approximation accuracy. Due to the emergence of the massive data, one is faced with an onerous computational burden for computing the regularization parameter via classical approaches (Gazzola and Sabaté Landman in GAMM-Mitteilungen 43:e202000017, 2020) such as the weighted generalized cross validation (WGCV) (Chung et al. in Electr Trans Numer Anal 28:2008, 2008), the unbiased predictive risk estimator (Stein in Ann Stat 9:1...