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Low-M-Rank Tensor Completion and Robust Tensor PCA

Bo Jiang(isyebojiang***at***gmail.com)
Shiqian Ma(sqma***at***math.ucdavis.edu)
Shuzhong Zhang(zhangs***at***umn.edu)

Abstract: In this paper, we propose a new approach to solve low-rank tensor completion and robust tensor PCA. Our approach is based on some novel notion of (even-order) tensor ranks, to be called the M-rank, the symmetric M-rank, and the strongly symmetric M-rank. We discuss the connections between these new tensor ranks and the CP-rank and the symmetric CP-rank of an even-order tensor. We show that the M-rank provides a reliable and easy-computable approximation to the CP-rank. As a result, we propose to replace the CP-rank by the M-rank in the low-CP-rank tensor completion and robust tensor PCA. Numerical results suggest that our new approach based on the M-rank outperforms existing methods that are based on low-n-rank, t-SVD and KBR approaches for solving low-rank tensor completion and robust tensor PCA when the underlying tensor has low CP-rank.


Category 1: Convex and Nonsmooth Optimization

Category 2: Nonlinear Optimization

Category 3: Applications -- Science and Engineering


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Entry Submitted: 10/05/2018
Entry Accepted: 10/05/2018
Entry Last Modified: 10/05/2018

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