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

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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.

AMS subject classifications

primary
62H25
62H30
secondary
34L20

Keywords

Consistency
Eigenvalue distribution
HDLSS
Microarray data analysis
Mixture model
Principal component analysis
Singular value

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