Combinatorics

Physics

Pattern recognition (psychology)

Tensor (intrinsic definition)

Singular value decomposition

Sparse PCA

Mathematics

Tucker decomposition

Matrix norm

Algorithm

Matrix (chemical analysis)

Singular value

Gaussian

Rank (graph theory)

Artificial intelligence

Eigenvalues and eigenvectors

Composite material

Principal component analysis

Materials science

Geometry

Robust principal component analysis

Tensor decomposition

Computer science

Sparse matrix

Quantum mechanics

Matrix decomposition

Low-rank approximation

IEEE Journal of Selected Topics in Signal Processing

Robust principal component analysis (RPCA) has been widely used for many data analysis problems in matrix data. Robust tensor principal component analysis (RTPCA) aims to extract the low rank and sparse components of multidimensional data, which is a generation of RPCA. The current RTPCA methods are directly based on tensor singular value decomposition (t-SVD), which is a new tensor decomposition method similar to singular value decomposition (SVD) in matrices. These methods focus on utilizing different sparse constraints for real applications and make less analysis for tensor nuclear norm (TNN) defined in t-SVD. However, we find low-rank structure still exists in the core tensor and existing methods can not fully extract the low-rank structure of tensor data. To further exploit the low-rank structures in multiway data, we extract low-rank component for the core matrix whose entries are from the diagonal elements of the core tensor. Based on this idea, we have defined a new TNN that extends TNN with core matrix and propose a creative algorithm to deal with RTPCA problems. The results of numerical experiments show that the proposed method outperforms state-of-the-art methods in terms of both accuracy and computational complexity.

Improved Robust Tensor Principal Component Analysis via Low-Rank Core Matrix