Effective PCA for high-dimension, low-sample-size data with noise reduction via geometric representations

Kazuyoshi Yata and Makoto Aoshima

Journal of Multivariate Analysis, 2012, vol. 105, issue 1, 193-215

Abstract: In this article, we propose a new estimation methodology to deal with PCA for high-dimension, low-sample-size (HDLSS) data. We first show that HDLSS datasets have different geometric representations depending on whether a ρ-mixing-type dependency appears in variables or not. When the ρ-mixing-type dependency appears in variables, the HDLSS data converge to an n-dimensional surface of unit sphere with increasing dimension. We pay special attention to this phenomenon. We propose a method called the noise-reduction methodology to estimate eigenvalues of a HDLSS dataset. We show that the eigenvalue estimator holds consistency properties along with its limiting distribution in HDLSS context. We consider consistency properties of PC directions. We apply the noise-reduction methodology to estimating PC scores. We also give an application in the discriminant analysis for HDLSS datasets by using the inverse covariance matrix estimator induced by the noise-reduction methodology.

Keywords: Consistency; Discriminant analysis; Eigenvalue distribution; Geometric representation; HDLSS; Inverse matrix; Noise reduction; Principal component analysis (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (17)

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DOI: 10.1016/j.jmva.2011.09.002

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