Effective PCA for high-dimension, low-sample-size data with singular value decomposition of cross data matrix

Authors:
Kazuyoshi Yata;Makoto Aoshima
Affiliations:
Graduate School of Pure and Applied Sciences, University of Tsukuba, Ibaraki 305-8571, Japan;Institute of Mathematics, University of Tsukuba, Ibaraki 305-8571, Japan
Venue:
Journal of Multivariate Analysis
Year:
2010

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Abstract

In this paper, we propose a new methodology to deal with PCA in high-dimension, low-sample-size (HDLSS) data situations. We give an idea of estimating eigenvalues via singular values of a cross data matrix. We provide consistency properties of the eigenvalue estimation as well as its limiting distribution when the dimension d and the sample size n both grow to infinity in such a way that n is much lower than d. We apply the new methodology to estimating PC directions and PC scores in HDLSS data situations. We give an application of the findings in this paper to a mixture model to classify a dataset into two clusters. We demonstrate how the new methodology performs by using HDLSS data from a microarray study of prostate cancer.