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Sparse PCA by iterative elimination algorithm

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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.

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Authors and Affiliations

  1. Department of Mathematics, Michigan State University, East Lansing, MI, 48824, USA

    Yang Wang

  2. Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, TN, 37132, USA

    Qiang Wu

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  1. Yang Wang
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  2. Qiang Wu
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Correspondence to Qiang Wu.

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Communicated by Charles Micchelli.

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Wang, Y., Wu, Q. Sparse PCA by iterative elimination algorithm. Adv Comput Math 36, 137–151 (2012). https://doi.org/10.1007/s10444-011-9186-3

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  • DOI: https://doi.org/10.1007/s10444-011-9186-3

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