Work

Tensor ring rank determination using odd-dimensional unfolding

Year: 2024

Type: article

Abstract: While tensor ring (TR) decomposition methods have been extensively studied, the determination of TR-ranks remains a challenging problem, with existing methods being typically sensitive to the determination of the starting rank (i.e., the first rank to be optimized). Moreover, current methods often fail to adaptively determine TR-ranks in the presence of noisy and incomplete data, and exhibit computational inefficiencies when handling high-dimensional data. To address these issues, we propose an odd-dimensional unfolding method for the effective determination of TR-ranks. This is achieved by leveraging the symmetry of the TR model and the bound rank relationship in TR decomposition. In addition, we employ the singular value thresholding algorithm to facilitate the adaptive determination of TR-ranks and use randomized sketching techniques to enhance the efficiency and scalability of the method. Extensive experimental results in rank identification, data denoising, and completion demonstrate the potential of our method for a broad range of applications.

Source: Neural Networks

DOI: 10.1016/j.neunet.2024.106947

Authors: Yichun Qiu, Guoxu Zhou, Chao Li, Danilo Mandic, Qibin Zhao

Institutions: Guangdong University of Technology, RIKEN Center for Advanced Intelligence Project, Juntendo University, Imperial College London

Language: English

Topic: Tensor decomposition and applications

Subfield: Computational Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,350

Funders: National Natural Science Foundation of China, Japan Society for the Promotion of Science, RIKEN