对称阵稀疏主成分分析及其在充分降维问题中的应用

J4 ›› 2012, Vol. 47 ›› Issue (4): 116-120.

对称阵稀疏主成分分析及其在充分降维问题中的应用

邵伟¹,祝丽萍²,刘福国^2,王秋平²

1.山东大学数学学院, 山东济南 250100; 2.昌吉学院数学系, 新疆昌吉 831100

收稿日期:2011-05-16 出版日期:2012-04-20 发布日期:2012-06-28
作者简介:邵伟(1983- ),男,博士研究生,研究方向为非参数统计、统计计算方法. Email:wshao1031@gmai.com
基金资助:
国家重点基础研究发展规划项目计划(973计划)项目(2007CB814900);昌吉学院研究群体项目(2011YJQT01);昌吉学院科学基金项目(2011YJYB005，2011SSQD002)

Sparse principal component analysis for symmetric matrix and application in sufficient dimension reduction

SHAO Wei¹, ZHU Li-ping^2, LIU Fu-Guo², WANG Qiu-Ping²

1. School of Mathimatics, Shandong University, Jinan 250100, Shandong, China;
2. Department of Mathematics, Changji College, Changji 831100, Xinjiang, China

Received:2011-05-16 Online:2012-04-20 Published:2012-06-28

摘要/Abstract

摘要：

讨论了对称阵的稀疏主成分分析,并给出估计的渐近结果。基于蒙特卡洛分析的模拟实验展示了在充分降维中稀疏主成分的优势。

关键词: 对称阵；主成分分析;稀疏主成分分析;充分降维；蒙特卡洛；LASSO

Abstract:

Sparse principal component analysis(SPC) for symmetric matrix and application are discussed. Asymptotic properties are obtained. Monte Carlo based simulations are used to illustrate the efficacy of the new method.

Key words: symmetric matrix; principal component analysis; sparse principal component analysis; sufficient dimension reduction; Monte Carlo; LASSO

邵伟1,祝丽萍2,刘福国2,王秋平2. 对称阵稀疏主成分分析及其在充分降维问题中的应用[J]. J4, 2012, 47(4): 116-120.

SHAO Wei1, ZHU Li-ping2, LIU Fu-Guo2, WANG Qiu-Ping2. Sparse principal component analysis for symmetric matrix and application in sufficient dimension reduction[J]. J4, 2012, 47(4): 116-120.

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