摘要
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.
作者
王蕾
李因果
夏利宇
WANG Lei;LI Yin -guo;XIA Li- yu(a.Ccntcr for Applicd Statistics,b.School of Statistics,1.Rcnmin Univcrsity of China,Bcijing 100872,China;School of Busincss,Jiangsu Normal Univcrsity,Xuzhou 221116,China)
出处
《统计与信息论坛》
CSSCI
北大核心
2018年第6期3-8,共6页
Journal of Statistics and Information
基金
国家社会科学基金项目<面板数据主成分分析统计模型扩展及其应用>(15BTJ033)
关键词
稀疏主成分分析
有监督主成分分析
主成分逆回归模型
拟合误差
预测误差
sparse principal component analysis
supervised principal component analysis
inverseregression implicating principal components
fitting error
prediction error