Half thresholding eigenvalue algorithm for semidefinite matrix completion
The semidefinite matrix completion（SMC） problem is to recover a low-rank positive semidefinite matrix from a small subset of its entries. It is well known but NP-hard in general. We first show that under some cases, SMC problem and S1/2relaxation model share a unique solution. Then we prove that the...
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| Veröffentlicht in: | Science China. Mathematics Jg. 58; H. 9; S. 2015 - 2032 |
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| Abstract | The semidefinite matrix completion（SMC） problem is to recover a low-rank positive semidefinite matrix from a small subset of its entries. It is well known but NP-hard in general. We first show that under some cases, SMC problem and S1/2relaxation model share a unique solution. Then we prove that the global optimal solutions of S1/2regularization model are fixed points of a symmetric matrix half thresholding operator. We give an iterative scheme for solving S1/2regularization model and state convergence analysis of the iterative sequence.Through the optimal regularization parameter setting together with truncation techniques, we develop an HTE algorithm for S1/2regularization model, and numerical experiments confirm the efficiency and robustness of the proposed algorithm. |
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| AbstractList | The semidefinite matrix completion (SMC) problem is to recover a low-rank positive semidefinite matrix from a small subset of its entries. It is well known but NP-hard in general. We first show that under some cases, SMC problem and S sub(1/2) relaxation model share a unique solution. Then we prove that the global optimal solutions of S sub(1/2) regularization model are fixed points of a symmetric matrix half thresholding operator. We give an iterative scheme for solving S sub(1/2) regularization model and state convergence analysis of the iterative sequence. Through the optimal regularization parameter setting together with truncation techniques, we develop an HTE algorithm for S sub(1/2) regularization model, and numerical experiments confirm the efficiency and robustness of the proposed algorithm. The semidefinite matrix completion（SMC） problem is to recover a low-rank positive semidefinite matrix from a small subset of its entries. It is well known but NP-hard in general. We first show that under some cases, SMC problem and S1/2relaxation model share a unique solution. Then we prove that the global optimal solutions of S1/2regularization model are fixed points of a symmetric matrix half thresholding operator. We give an iterative scheme for solving S1/2regularization model and state convergence analysis of the iterative sequence.Through the optimal regularization parameter setting together with truncation techniques, we develop an HTE algorithm for S1/2regularization model, and numerical experiments confirm the efficiency and robustness of the proposed algorithm. The semidefinite matrix completion (SMC) problem is to recover a low-rank positive semidefinite matrix from a small subset of its entries. It is well known but NP-hard in general. We first show that under some cases, SMC problem and S 1/2 relaxation model share a unique solution. Then we prove that the global optimal solutions of S 1/2 regularization model are fixed points of a symmetric matrix half thresholding operator. We give an iterative scheme for solving S 1/2 regularization model and state convergence analysis of the iterative sequence. Through the optimal regularization parameter setting together with truncation techniques, we develop an HTE algorithm for S 1/2 regularization model, and numerical experiments confirm the efficiency and robustness of the proposed algorithm. |
| Author | CHEN YongQiang LUO ZiYan XIU NaiHua |
| AuthorAffiliation | Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China The State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044, China |
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| Keywords | semidefinite matrix completion convergence relaxation 90C06 half thresholding eigenvalue algorithm 90C26 90C59 |
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| Notes | semidefinite matrix completion;S1/2relaxation;half thresholding eigenvalue algorithm;conver-gence 11-5837/O1 The semidefinite matrix completion（SMC） problem is to recover a low-rank positive semidefinite matrix from a small subset of its entries. It is well known but NP-hard in general. We first show that under some cases, SMC problem and S1/2relaxation model share a unique solution. Then we prove that the global optimal solutions of S1/2regularization model are fixed points of a symmetric matrix half thresholding operator. We give an iterative scheme for solving S1/2regularization model and state convergence analysis of the iterative sequence.Through the optimal regularization parameter setting together with truncation techniques, we develop an HTE algorithm for S1/2regularization model, and numerical experiments confirm the efficiency and robustness of the proposed algorithm. ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
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| Snippet | The semidefinite matrix completion（SMC） problem is to recover a low-rank positive semidefinite matrix from a small subset of its entries. It is well known... The semidefinite matrix completion (SMC) problem is to recover a low-rank positive semidefinite matrix from a small subset of its entries. It is well known but... |
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| SubjectTerms | Algorithms Applications of Mathematics Convergence Eigenvalues Iterative methods Mathematical models Mathematics Mathematics and Statistics Optimization Regularization Robustness 全局最优解 半正定矩阵 参赛作品 对称矩阵 收敛性分析 特征值 算法 阈值 |
| Title | Half thresholding eigenvalue algorithm for semidefinite matrix completion |
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