Efficient Numerical Solution for Constrained Tensor Ring Decomposition: A Theoretical Convergence Analysis and Applications

2022 Fiscal Year Final Research Report

• Project/Area Number: 20K19749
• Research Category: Grant-in-Aid for Early-Career Scientists
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 60020:Mathematical informatics-related
• Research Institution: The Institute of Statistical Mathematics
• Principal Investigator: Zheng Ning 統計数理研究所, 統計的機械学習研究センター, 特任研究員 (60859122)
• Project Period (FY): 2020-04-01 – 2023-03-31
• Keywords: iterative method / tensor / convergence / nonnegative / random

Outline of Final Research Achievements

(1) For solving the least squares subproblems of tensor-based optimization problem, we propose a randomized and greedy Kaczmarz-type inner-iteration preconditioned flexible GMRES method.
(2) For handling the ill-posed tensor network, we consider graph-regularized tensor-ring with nonnegativity. The proposed models extend tensor ring decomposition and can be served as powerful representation learning tools for non-negative multiway data.

Free Research Field

Numerical linear algebra

Academic Significance and Societal Importance of the Research Achievements

Extracting meaningful and interpretable low-dimensional representation from high-dimensional data is a fundamental task in the fields of signal processing and machine learning. Our research provide robust mathematical tools for handling some computational and application problems.