On the Structure of the Quadratic Subspace in Discriminant Analysis Articles uri icon

publication date

  • May 2010

start page

  • 1239

end page

  • 1251

issue

  • 5

volume

  • 101

international standard serial number (ISSN)

  • 0047-259X

electronic international standard serial number (EISSN)

  • 1095-7243

abstract

  • The concept of quadratic subspace is introduced as a helpful tool for dimension reduction in quadratic discriminant analysis (QDA). It is argued that an adequate representation of the quadratic subspace may
    lead to better methods for both data representation and classification.
    Several theoretical results describe the structure of the quadratic
    subspace, that is shown to contain some of the subspaces previously
    proposed in the literature for finding differences between the class
    means and covariances. A suitable assumption of orthogonality between
    location and dispersion subspaces allows us to derive a convenient
    reduced version of the full QDA rule. The behavior of these ideas in
    practice is illustrated with three real data examples.