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Topic: Numerical Issues about Computation of log likelihood in High Dimension
Replies: 0

 Cem DEMiRKIR Posts: 1 From: TURKiYE(TURKEY) Registered: 5/17/06
Numerical Issues about Computation of log likelihood in High Dimension
Posted: May 17, 2006 3:20 AM

Dear Community Members
I'd like to compute likelihood score sum of the clustering made by KMeans algorithm by assuming that each cluster is a gaussian distributed samples. When I compute the likelihood for a sample using the following negatif log-likelihood formula

log-Likelihood = (x-mu)'*SigmaInv*(x-mu) + (d/2)ln(2pi)
+ (1/2)ln |SigmaInv|

where x : sample vector, mu : cluster mean sample vector, d : dimension of the sample vectors, SigmaInv : inverse of the covariance matrix sigma, the determinant of the |SigmaInv| goes beyond the numerical limit of the computer, and gives infinity error since d is very high such as about 400. What can be done to overcome this numerical problem and to compute the likelihoods of the samples ?

Sincerely
Cem DEMiRKIR