Work

A new algorithm by embedding structured data for low-rank tensor ring completion

Year: 2025

Type: article

Abstract: In this paper, we put up with a new algorithm for tensor completion problems that include missing slices or row/column fibers, where embedding a structured tensor by a multi-way delay-embedding transform (MDT) makes the tensor to be completed have a special structure. The main idea is to employ a tensor completion algorithm based on the tensor ring rank, constructing latent tensor ring factors with a structure that approximates the original tensor starting from the tensor structure. It is also proved that the sequence generated by the new algorithm converges to the optimal solution. Finally, the feasibility of the proposed algorithm is verified by experiments. Compared with other completed algorithms based on tensor ring rank, the completed accuracy is improved, up to 30%.

Source: AIMS Mathematics

DOI: 10.3934/math.2025297

Authors: Ruiping Wen, Tingyan Liu, Yalei Pei

Institution: Taiyuan Normal University

Language: English

Topic: Tensor decomposition and applications

Subfield: Computational Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,200

Funders: National Science Foundation, National Natural Science Foundation of China