Sparse PCA by iterative elimination algorithm

Authors:
Yang Wang;Qiang Wu
Affiliations:
Department of Mathematics, Michigan State University, East Lansing, USA 48824;Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, USA 37132
Venue:
Advances in Computational Mathematics
Year:
2012

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Abstract

In this paper we proposed an iterative elimination algorithm for sparse principal component analysis. It recursively eliminates variables according to certain criterion that aims to minimize the loss of explained variance, and reconsiders the sparse principal component analysis problem until the desired sparsity is achieved. Two criteria, the approximated minimal variance loss (AMVL) criterion and the minimal absolute value criterion, are proposed to select the variables eliminated in each iteration. Deflation techniques are discussed for multiple principal components computation. The effectiveness is illustrated by both simulations on synthetic data and applications on real data.