Re: eigenvalues in LDA


In article <e282c84c-ca73-4f3a-8afa-f9af503a0c1a@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Geordie <camusartre@xxxxxxxxx> writes:
hello, the problem I'm dealing with is finding eigenvalues and
eigenvectors of a
real, non-simmetric matrix, to perform Linear Discrminant Analysis of
data.
I know it is possible to find them by reducing the matrix to
Hessenberg form ("Numerical recipes in C").
But now I'm facing the problem of selecting the largest eigenvalues
(that's what LDA theory says): as they can be complex, should I choose
the largest modules?
Thanks to anyboddy can help me
geordie


if the matrix isn't really large (n>500 say) then don't care
much about it: use the general QR algorithm (e.g. from LAPACK)
which gets all eigenvalues and eigenvectors and select the one you need.
otherwise, things become a bit more tricky:
iterative solvers for selected eigenpairs can find the
largest in modulus , the smallest in modulus or some eigenpairs near
a given value (in the complex plane) but these are not necessarily
the algebraic largest (with respect to the real part in the complex case,
for example).
if the "largest" you are behind is not necessarily the largest
in modulus, you first must apply a decent shift of the spectrum
to make this the case.
then you could apply for example arpack
hth
peter

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