Eigenvectors of a Kurtosis Matrix as Interesting Directions to Reveal Cluster Structure Articles uri icon

publication date

  • October 2010

start page

  • 1995

end page

  • 2007

issue

  • 9

volume

  • 101

international standard serial number (ISSN)

  • 0047-259X

electronic international standard serial number (EISSN)

  • 1095-7243

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.