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Topic:
Numerical Issues about Computation of log likelihood in High Dimension
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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 loglikelihood formula
logLikelihood = (xmu)'*SigmaInv*(xmu) + (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



