English, Article edition: Invariant co-ordinate selection David E. Tyler; Frank Critchley; Lutz Dümbgen; ...

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Bookmark: http://trove.nla.gov.au/version/107619
Physical Description
  • article
Language
  • English

Edition details

Title
  • Invariant co-ordinate selection
Author
  • David E. Tyler
  • Frank Critchley
  • Lutz Dümbgen
  • Hannu Oja
Physical Description
  • article
Notes
  • A general method for exploring multivariate data by comparing different estimates of multivariate scatter is presented. The method is based on the eigenvalue-eigenvector decomposition of one scatter matrix relative to another. In particular, it is shown that the eigenvectors can be used to generate an affine invariant co-ordinate system for the multivariate data. Consequently, we view this method as a method for "invariant co-ordinate selection". By plotting the data with respect to this new invariant co-ordinate system, various data structures can be revealed. For example, under certain independent components models, it is shown that the invariant co- ordinates correspond to the independent components. Another example pertains to mixtures of elliptical distributions. In this case, it is shown that a subset of the invariant co-ordinates corresponds to Fisher's linear discriminant subspace, even though the class identifications of the data points are unknown. Some illustrative examples are given. Copyright (c) 2009 Royal Statistical Society.
  • RePEc:bla:jorssb:v:71:y:2009:i:3:p:549-592
Language
  • English
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