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Low-M-Rank Tensor Completion and Robust ...
Jiang, Bo...

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Low-M-Rank Tensor Completion and Robust Tensor PCA by Jiang, Bo ( Author )
Lemonjar Open Access
Australian National University
07-09-2023
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.
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Article
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29.34 KB
English
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MYR 0.01
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http://arxiv.org/abs/1501.03689
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