Efficient Numerical Solution for Constrained Tensor Ring Decomposition: A Theoretical Convergence Analysis and Applications
| Project/Area Number |
20K19749
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| Research Category |
Grant-in-Aid for Early-Career Scientists
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| Allocation Type | Multi-year Fund |
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| Review Section |
Basic Section 60020:Mathematical informatics-related
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| Research Institution | The Institute of Statistical Mathematics |
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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)
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| Project Period (FY) |
2020-04-01 – 2023-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2022: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2021: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2020: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | iterative method / tensor / convergence / nonnegative / random / ill-posed problem / ADMM / nonnegative constraints / tensor learning / randomized algorithm / graph regularization / linear system / iterative methods / preconditioning / randomized / consistent / linear systems / nonconvex / nonnegative constraint / convergence theory |
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| Outline of Research at the Start |
The outline of this research is listed as following three aspects. Firstly, efficient numerical algorithms for nonconvex tensor ring decomposition with nonnegative, graph, sparsity and smoothness constraints are studied and constructed. Secondly, theoretical convergence analysis of the numerical algorithms, including the computational complexity analysis and the sufficient conditions of local and global convergence are proposed. Thirdly, the proposed robust algorithms are applied for low-rank tensor based applications, especially on hyperspectral image tensor completion and video restoration.
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| 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.
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| 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.
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Report
(4 results)
Research Products
(6 results)
