T-product factorization based method for matrix and tensor completion problems

Quan Yu () and Xinzhen Zhang ()
Additional contact information
Quan Yu: Hunan University
Xinzhen Zhang: Tianjin University

Computational Optimization and Applications, 2023, vol. 84, issue 3, No 4, 788 pages

Abstract: Abstract Low rank matrix and tensor completion problems are to recover the incomplete two and higher order data of low rank structures. The essential problem in the matrix and tensor completion problems is how to improve the efficiency. For a matrix completion problem, we establish a relationship between matrix rank and tensor tubal rank, and reformulate matrix completion problem as a third order tensor completion problem. For the reformulated tensor completion problem, we adopt a two-stage strategy based on tensor factorization algorithm. In this way, a matrix completion problem of big size can be solved via some matrix computations of smaller sizes. For a third order tensor completion problem, to fully exploit the low rank structures, we introduce the double tubal rank which combines the tubal rank of two tensors, original tensor and the reshaped tensor of the mode-3 unfolding matrix of original tensor. Based on this, we propose a reweighted tensor factorization algorithm for third order tensor completion. Extensive numerical experiments demonstrate that the proposed methods outperform state-of-the-art methods in terms of both accuracy and running time.

Keywords: Matrix completion; Tensor completion; Tensor factorization; Tubal rank (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10589-022-00439-y Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:coopap:v:84:y:2023:i:3:d:10.1007_s10589-022-00439-y

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-022-00439-y

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

More articles in Computational Optimization and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().