If we assume that the input data matrix
, containing the samples from
different populations
.
A vital assumption made when applying the LDA method is that the
covariance matrices for each of the
populations are
equal, and of full rank, i.e
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If these matrices are not of full rank, they can be replaced by
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If we consider the linear combination given by
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|
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||
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Letting
donate the sample
data set from population, we define the sample mean vector as
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Now let
denote the
nonzero eigenvalues of
with corresponding
eigenvectors
, scaled
s.t
. Then the vector of coefficients
that maximizes the ratio
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A classification rule based on the first sample
discriminants is as follows, [1]:
Allocate
to population
if
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Bjørn Kåre Alsberg 2006-04-06