基于连接函数的投影寻踪主成分分析  

Analyses of projection pursuit principal components based on Copulas

作　　者：王晓光[1] 宋立新[1] 

机构地区：[1]大连理工大学数学科学学院

出　　处：《大连理工大学学报》2011年第5期771-776,共6页Journal of Dalian University of Technology

基　　金：大连理工大学引进人才科研启动经费资助项目(3004-852001)

摘　　要：基于连接函数的相依度量，提出了一种探索连续型随机向量之间相关关系的方法．通过连接函数构造的投影指标函数可以给出高维随机向量的投影寻踪主成分分析，并且可以证明这样得到的最优样本投影方向具有强相合性．此外，又给出了两个以上随机向量之间的典型相关分析．结果表明所提出的方法具有优良的理论性和实用前景．An approach to exploring the dependence relation of continuous random vectors is presented based on the dependence measure constructed by Copula. Copula is used to construct the index function in the analyses of the projection pursuit principal components with high-dimensional random vector, and the obtained optimal projection directions are strong consistency. In addition, the canonical correlation analyses of two or more random vectors are discussed. The conclusions show that the proposed method has excellent theoretical properties and practical prospects.

关 键 词：投影寻踪 连接函数 经验连接函数 主成分分析 典型相关分析 

分 类 号：O212.4[理学—概率论与数理统计]