On General Adaptive Sparse Principal Component Analysis

Journal of Computational and Graphical Statistics, Forthcoming

20 Pages Posted: 1 Dec 2008

See all articles by Chenlei Leng

Chenlei Leng

University of Warwick

Hansheng Wang

Peking University - Guanghua School of Management

Date Written: November 27, 2008

Abstract

The method of sparse principal component analysis (S-PCA) proposed by Zou et al. (2006) is an attractive approach to obtain sparse loadings in principal component analysis (PCA). SPCA was motivated by reformulating PCA as a least squares problem so that a lasso penalty on the loading coefficients can be applied. In this article, we propose new estimates to improve S-PCA on the following two aspects. Firstly, we propose a method of simple adaptive sparse principal component analysis (SAS-PCA), which uses the adaptive lasso penalty (Zou, 2006; Wang et al., 2007) instead of the lasso penalty in S-PCA. Secondly, we replace the least squares objective function in S-PCA by a general least squares objective function. This formulation allows us to study many related sparse PCA estimators under a unified theoretical framework and leads to the method of general adaptive sparse principal component analysis (GAS-PCA). Compared with SAS-PCA, GAS-PCA enjoys much further improved finite sample performance. In addition to that, we show that when a BIC-type criterion is used for selecting the tuning parameters, the resulting estimates are consistent in variable selection. Numerical studies are conducted to compare the finite sample performance of various competing methods.

Keywords: Adaptive Lasso, BIC, GAS-PCA, LARS, Lasso, S-PCA, SAS-PCA

JEL Classification: C5, C52

Suggested Citation

Leng, Chenlei and Wang, Hansheng, On General Adaptive Sparse Principal Component Analysis (November 27, 2008). Journal of Computational and Graphical Statistics, Forthcoming. Available at SSRN: https://ssrn.com/abstract=1308324

Chenlei Leng

University of Warwick ( email )

Gibbet Hill Rd.
Coventry, West Midlands CV4 8UW
United Kingdom

Hansheng Wang (Contact Author)

Peking University - Guanghua School of Management ( email )

Peking University
Beijing, Beijing 100871
China

HOME PAGE: http://hansheng.gsm.pku.edu.cn

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