Tensor Robust Principal Component Analysis with a New Tensor Nuclear Norm

Lu, Canyi; Feng, Jiashi; Chen, Yudong; Liu, Wei; Lin, Zhouchen; Yan, Shuicheng

doi:10.1109/tpami.2019.2891760

articleIEEE Transactions on Pattern Analysis and Machine IntelligenceJan 9, 2019Closed access

Tensor Robust Principal Component Analysis with a New Tensor Nuclear Norm

CLCanyi Lu JFJiashi Feng YCYudong Chen WLWei Liu ZLZhouchen Lin

Carnegie Mellon University · National University of Singapore · +3 more institutions

PubMed

Indexed incrossrefpubmed

Abstract

In this paper, we consider the Tensor Robust Principal Component Analysis (TRPCA) problem, which aims to exactly recover the low-rank and sparse components from their sum. Our model is based on the recently proposed tensor-tensor product (or t-product) [14]. Induced by the t-product, we first rigorously deduce the tensor spectral norm, tensor nuclear norm, and tensor average rank, and show that the tensor nuclear norm is the convex envelope of the tensor average rank within the unit ball of the tensor spectral norm. These definitions, their relationships and properties are consistent with matrix cases. Equipped with the new tensor nuclear norm, we then solve the TRPCA problem by solving a convex program and…

Citation impact

1,095

total citations

FWCI: 84.27
Percentile: 100%
References: 38

Citations per year

Authors

6

Topics & keywords

Topics

Keywords

Robust principal component analysis
Matrix norm
Cartesian tensor
Tensor density
Tensor (intrinsic definition)
Tensor product of Hilbert spaces
Tensor contraction
Mathematics

No related works found for this paper.