[SciPy-User] cholesky

Gael Varoquaux gael.varoquaux@normalesup....
Sun Apr 25 04:47:11 CDT 2010


On Fri, Apr 23, 2010 at 10:15:35AM +0100, alexander baker wrote:
>    We have computed a decomposition matrix using the cholesky method for a
>    correlation matrix, some of the eigenvalues are negative and we set those
>    to zero, the question is how can we estimate the significance of removing
>    these eigenvalues from the original correlation matrix?

I am not sure what you mean by 'the signification'. A correlation matrix
with negative eigenvalues is an undefined correlation matrix: it
corresponds to an impossible signal (you are most probably ending up in
such a situation because you did not have enough independent data samples
to estimate the correlation matrix).

The best thing you can do, IMHO, is to regularise the correlation matrix.
In my experience, the Ledoit-Wolf regularisation works really well:
www.ledoit.net/honey.pdf

I have some code to apply this regularisation, but it is not terribly
performant (could probably be improved).

Out of curiosity: in what context are you using these correlation
matrices? What is your final use case?

HTH,

Gaël


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