一种新的相关系数矩阵稀疏估计的对偶方法

薛文娟; 刘潇

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DOI:10.3969/j.issn.2096-8299.2022.01.016

Journal of ShangHai University of Electric Power :2022,38(1):98-104

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一种新的相关系数矩阵稀疏估计的对偶方法

薛文娟¹, 刘潇²

(1.上海电力大学数理学院;2.上海理工大学理学院)

A New Dual Method for the Sparse Estimation of Correlation Matrices

XUE Wenjuan¹, LIU Xiao²

(1.School of Mathematics and Physics, Shanghai University of Electric Power, Shanghai 200090, China;2.College of Science, University of Shanghai for Science and Technology, Shanghai 200439, China)

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Received:November 06, 2021

中文摘要: 提出了一种新的基于邻近梯度的对偶方法。该方法求解Frobenius范数意义下的相关系数矩阵的稀疏逼近问题。首先, 推导出一种新的有界约束的对偶问题; 然后, 提出一个相应的具有全局收敛性的邻近梯度算法; 最后, 通过在随机数据集上的数值结果验证了该算法的可行性。

中文关键词: 相关系数矩阵稀疏逼近对偶邻近梯度算法全局收敛性

Abstract:In this paper, we propose a novel dual method based on proximal gradient method for the sparse approximation of correlation matrices in the sense of Frobenius norm.A new dual formulation with bound constraints is derived.To solve the dual, a global convergent proximal gradient algorithm is developed.Some preliminary numerical results on synthetic data sets are given to confirm the feasibility of our algorithm.

keywords: correlation matrices sparse approximation dual proximal gradient algorithm global convergence

文章编号：20221016 中图分类号：O221 文献标志码：

基金项目:国家自然科学基金青年项目(11601318)

Author Name	Affiliation	E-mail
XUE Wenjuan	School of Mathematics and Physics, Shanghai University of Electric Power, Shanghai 200090, China	xuewenjuan@shiep.edu.cn
LIU Xiao	College of Science, University of Shanghai for Science and Technology, Shanghai 200439, China

Author Name	Affiliation	E-mail
XUE Wenjuan	School of Mathematics and Physics, Shanghai University of Electric Power, Shanghai 200090, China	xuewenjuan@shiep.edu.cn
LIU Xiao	College of Science, University of Shanghai for Science and Technology, Shanghai 200439, China

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