基于正交迭代的有监督的稀疏主成分分析

Supervised Sparse Principal Component Analysis Based on Orthogonal Iteration

主成分分析是经典的无监督的数据处理工具,近年来关于稀疏主成分和有监督的主成分研究受到较多关注。基于正交迭代和距离相关系数,提出一种有监督的稀疏主成分分析方法 SSPCA,该方法考虑了自变量与因变量之间的相关性,并在迭代求解的过程中将一些与因变量Y相关性很弱的自变量对应的系数变为0,使所求的特征向量只保留预测能力较强的自变量信息;在数值模拟与实例分析中,相比其他四种方法,SSPCA方法均能取得较好效果。

Principal component analysis is a classical unsupervised data processing tool.In recent years,research on sparse and supervised principal component analysis have raised much attention.Based on orthogonal iteration and distance correlation,this paper proposes a supervised sparse principal component analysis,SSPCA.SSPCA takes the correlation between response and predictors into account,and sets the coefficients of predictors that less correlated to the response to zero during iteration,making eigenvectors obtained only contain predictors strongly correlated to Y.In numeric studies and real data analysis,SSPCA performs better than other four methods.