Sparse principal component regression with adaptive loading

被引：21

作者：

Kawano, Shuichi ^{[1
,4
]}

Fujisawa, Hironori ^{[2
,4
]}

Takada, Toyoyuki ^{[3
,4
]}

Shiroishi, Toshihiko ^{[3
,4
]}

机构：

[1] Univ Electrocommun, Grad Sch Informat Syst, Tokyo 1828585, Japan

[2] Inst Stat Math, Tachikawa, Tokyo 1908562, Japan

[3] Natl Inst Genet, Mammalian Genet Lab, Mishima, Shizuoka 4118540, Japan

[4] Res Org Informat & Syst, Transdisciplinary Res Integrat Ctr, Minato Ku, Tokyo 1050001, Japan

来源：

COMPUTATIONAL STATISTICS & DATA ANALYSIS | 2015年 / 89卷

关键词：

Dimension reduction; Identifiability; Principal component regression; Regularization; Sparsity; SIMULTANEOUS DIMENSION REDUCTION; VARIABLE SELECTION; REGULARIZATION;

D O I：

10.1016/j.csda.2015.03.016

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

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.

引用

页码：192 / 203

页数：12

共 32 条

[1] Regularized Partial Least Squares with an Application to NMR Spectroscopy
Allen, Genevera I.
Peterson, Christine
Vannucci, Marina
Maletic-Savatic, Mirjana
[J]. STATISTICAL ANALYSIS AND DATA MINING, 2013, 6 (04) : 302 - 314
[2] [Anonymous], 1975, Perspectives in probability and statistics
[3] Prediction by supervised principal components
Bair, E
Hastie, T
Paul, D
Tibshirani, R
[J]. JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 2006, 101 (473) : 119 - 137
[4] Sparse Reduced-Rank Regression for Simultaneous Dimension Reduction and Variable Selection
Chen, Lisha
Huang, Jianhua Z.
[J]. JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 2012, 107 (500) : 1533 - 1545
[5] Choi J, 2010, STAT INTERFACE, V3, P429
[6] Sparse partial least squares regression for simultaneous dimension reduction and variable selection
Chun, Hyonho
Keles, Suenduez
[J]. JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY, 2010, 72 : 3 - 25
[7] SIMPLS - AN ALTERNATIVE APPROACH TO PARTIAL LEAST-SQUARES REGRESSION
DEJONG, S
[J]. CHEMOMETRICS AND INTELLIGENT LABORATORY SYSTEMS, 1993, 18 (03) : 251 - 263
[8] Least angle regression - Rejoinder
Efron, B
Hastie, T
Johnstone, I
Tibshirani, R
[J]. ANNALS OF STATISTICS, 2004, 32 (02) : 494 - 499
[9] A STATISTICAL VIEW OF SOME CHEMOMETRICS REGRESSION TOOLS
FRANK, IE
FRIEDMAN, JH
[J]. TECHNOMETRICS, 1993, 35 (02) : 109 - 135
[10] Regularization Paths for Generalized Linear Models via Coordinate Descent
Friedman, Jerome
Hastie, Trevor
Tibshirani, Rob
[J]. JOURNAL OF STATISTICAL SOFTWARE, 2010, 33 (01): : 1 - 22

← 1 2 3 4 →