Low-M-Rank Tensor Completion and Robust Tensor PCA
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.
Cite
@article{arxiv.1501.03689,
title = {Low-M-Rank Tensor Completion and Robust Tensor PCA},
author = {Bo Jiang and Shiqian Ma and Shuzhong Zhang},
journal= {arXiv preprint arXiv:1501.03689},
year = {2018}
}