Publication: Eigenvectors of a kurtosis matrix as interesting directions to reveal cluster structure
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2010-10
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Elsevier
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Abstract
In this paper we study the properties of a kurtosis matrix and propose its eigenvectors
as interesting directions to reveal the possible cluster structure of a data set. Under a
mixture of elliptical distributions with proportional scatter matrix, it is shown that a
subset of the eigenvectors of the fourth-order moment matrix corresponds to Fisher's linear
discriminant subspace. The eigenvectors of the estimated kurtosis matrix are consistent
estimators of this subspace and its calculation is easy to implement and computationally
efficient, which is particularly favourable when the ratio n/p is large.
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Keywords
Cluster analysis, Dimension reduction, Fisher subspace, Kurtosis matrix, Multivariate kurtosis, Projection pursuit
Bibliographic citation
Journal of Multivariate Analysis, 2010, v. 101, n. 9 (oct. 2010), p. 1995-2007