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Invariant co-ordinate selection (with discussion)

Tyler, David E.; Critchley, Frank; Dümbgen, Lutz and Oja, Hannu (2009). Invariant co-ordinate selection (with discussion). Journal of the Royal Statistical Society: Series B (Statistical Methodology), 71(3) pp. 549–592.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1111/j.1467-9868.2009.00706.x
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Abstract

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.

Item Type: Journal Article
Copyright Holders: 2009 Royal Statistical Society
ISSN: 1467-9868
Keywords: affine invariance; cluster analysis; independent components analysis; mixture models; multivariate diagnostics; multivariate scatter; principal components; projection pursuit; robust statistics
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 26078
Depositing User: Frank Critchley
Date Deposited: 11 Jan 2011 17:33
Last Modified: 30 Oct 2013 10:55
URI: http://oro.open.ac.uk/id/eprint/26078
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