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

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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.

Journal

  • Journal of multivariate analysis

    Journal of multivariate analysis 105(1), 193-215, 2012-02

    Elsevier

Cited by:  1

Keywords

Codes

  • NII Article ID (NAID)
    120003439660
  • NII NACSIS-CAT ID (NCID)
    AA0025295X
  • Text Lang
    ENG
  • Article Type
    Journal Article
  • ISSN
    0047-259X
  • Data Source
    CJPref  IR 
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