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Workshop:
" Statistical data mining between research and practice
"
27./28. Februar 2004 in Hamburg
Angelika van der Linde
(Institute for Statistics, University of Bremen)
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Dimension Reduction with Linear Discriminant Functions
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For two random vectors X and Y the mutual information is defined to be
the Kullback-Leibler distance between the joint density of X and Y and
the product of their marginal densities. Under the assumption of
bi-affinity of the log-odds ratio function (characterizing the
association between X and Y) the symmetrized mutual information can be
represented as trace of the product of a parameter matrix and the
covariance matrix of X and Y. The assumption of bi-affinity is
immediately met by multivariate Normal and multinomial distributions but
is also often used in (logistic) regression models .
It is shown that eigendecompositions of the matrix underlying the
symmetrized mutual information yield familiar multivariate techninques
like canonical correlation analysis or Fisher's linear discriminant
functions under special distributional assumptions. Such
eigendecompositions are then suggested more generally as techniques of
dimension reduction with generalized linear discriminant functions.
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