Low-Rank Tensor Completion by Truncated Nuclear Norm Regularization

Xue, Shengke; Qiu, Wenyuan; Liu, Fan; Jin, Xinyu

doi:10.48550/arxiv.1712.00704

Cited by 1 publication

(1 citation statement)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recently, the t-SVD and the corresponding tensor tubal rank (and multi rank) have received considerable attentions [37][38][39][43][44][45][46][47][48][49][50][51][52][53]. As a generalization of the matrix singular value decomposition (SVD), the t-SVD regards a three-way tensor X as a matrix, each element of which is a tube (mode-3 fiber), and then decomposes X as X = U * S * V T , where U and V are orthogonal tensors, S is a f-diagonal tensor, V T denotes the conjugate transpose of V, and * denote the t-product (see details in Section 2).…”

Section: Introductionmentioning

confidence: 99%

Tensor N-tubal rank and its convex relaxation for low-rank tensor recovery

Zheng

Huang

Jiang

et al. 2018

Preprint

View full text Add to dashboard Cite

As low-rank modeling has achieved great success in tensor recovery, many research efforts devote to defining the tensor rank. Among them, the recent popular tensor tubal rank, defined based on the tensor singular value decomposition (t-SVD), obtains promising results. However, the framework of the t-SVD and the tensor tubal rank are applicable only to three-way tensors and lack of flexibility to handle different correlations along different modes. To tackle these two issues, we define a new tensor unfolding operator, named modek 1 k 2 tensor unfolding, as the process of lexicographically stacking the mode-k 1 k 2 slices of an N -way tensor into a three-way tensor, which is a three-way extension of the well-known mode-k tensor matricization. Based on it, we define a novel tensor rank, the tensor N -tubal rank, as a vector whose elements contain the tubal rank of all mode-k 1 k 2 unfolding tensors, to depict the correlations along different modes. To efficiently minimize the proposed N -tubal rank, we establish its convex relaxation: the weighted sum of tensor nuclear norm (WSTNN). Then, we apply WSTNN to low-rank tensor completion (LRTC) and tensor robust principal component analysis (TRPCA). The corresponding WSTNN-based LRTC and TRPCA models are proposed, and two efficient alternating direction method of multipliers (ADMM)-based algorithms are developed to solve the proposed models. Numerical experiments demonstrate that the proposed models significantly outperform the compared ones.Keywords: Low-rank tensor recovery (LRTR), mode-k 1 k 2 tensor unfolding, the tensor N -tubal rank, the weighted sum of tensor nuclear norm (WSTNN), alternating direction method of multipliers (ADMM).

show abstract