Sparse principal component regression with adaptive loading

作     者：Kawano, Shuichi Fujisawa, Hironori Takada, Toyoyuki Shiroishi, Toshihiko 

作者机构：Univ Electrocommun Grad Sch Informat Syst Tokyo 1828585 Japan Inst Stat Math Tachikawa Tokyo 1908562 Japan Natl Inst Genet Mammalian Genet Lab Mishima Shizuoka 4118540 Japan Res Org Informat & Syst Transdisciplinary Res Integrat Ctr Minato Ku Tokyo 1050001 Japan 

出 版 物：《COMPUTATIONAL STATISTICS & DATA ANALYSIS》 (计算统计学与数据分析)

年 卷 期：2015年第89卷

页      面：192-203页

核心收录：

学科分类：08[工学] 0714[理学-统计学（可授理学、经济学学位）] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：Bio-diversity Research Project of the Transdisciplinary Research Integration Center, Research Organization of Information and Systems Grants-in-Aid for Scientific Research [25430097, 15K15947] Funding Source: KAKEN 

主　　题：Dimension reduction Identifiability Principal component regression Regularization Sparsity 

摘      要：Principal component regression (PCR) is a two-stage procedure that selects some principal components and then constructs a regression model regarding them as new explanatory variables. Note that the principal components are obtained from only explanatory variables and not considered with the response variable. To address this problem, we propose the sparse principal component regression (SPCR) that is a one-stage procedure for PCR. SPCR enables us to adaptively obtain sparse principal component loadings that are related to the response variable and select the number of principal components simultaneously. SPCR can be obtained by the convex optimization problem for each parameter with the coordinate descent algorithm. Monte Carlo simulations and real data analyses are performed to illustrate the effectiveness of SPCR. (C) 2015 Elsevier B.V. All rights reserved.