Gaussian mixture model - Matlab parameter training

Hillel

I am running a speech enhancement algorithm based on Gaussian mixture model. The problem is that the estimation algorithm underflows during training. XI am trying to calculate the product of the PDF of each frequnecy component of the Gaussian cluster given by the PDF of the logarithmic spectrum X_k(FFT function is done with K = 1..256) What I get is a product 256 exp(-v(k))such thatv(k)>=0

Here is a snippet of a MATLAB calculation: N- number of frames; M- number of mixtures; c_iweight of each mixture;

gamma(n,i) = c_i*f(X_n|I = i)

 for i=1 : N
    rep_DataMat(:,:,i) = repmat(DataMat(:,i),1,M); 
    gamma_exp(:,:) = (1./sqrt((2*pi*sigmaSqr_curr))).*exp(((-1)*((rep_DataMat(:,:,i) - mue_curr).^2)./(2*sigmaSqr_curr)));
    gamma_curr(i,:) = c_curr.*(prod(10*gamma_exp(:,:),1));
    alpha_curr(i,:) = gamma_curr(i,:)./sum(gamma_curr(i,:));
end

Since K = 256, the factor is less than 1, so the product quickly goes to zero. Is there a way to calculate the result that causes the underflow (eg logum or similar)?

detective eye

You can perform calculations in the log domain.

The conversion of the product product is simple. On the other hand, sum can be converted with something like logumexp . This works using the following formula:

log(a + b) = log(exp(log(a)) + exp(log(b)))
           = log(exp(loga) + exp(logb))

where logaand logbin the respective representation a, and bin the logarithmic domain. Then, the basic idea is to decompose the exponent with the largest independent variable (for example, logafor illustration purposes):

 log(exp(loga)+exp(logb)) = log(exp(loga)*(1+exp(logb-loga)))
                          = loga + log(1+exp(logb-loga))

Note that the same idea applies if more than two terms are to be added.

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Hillel I am running a speech enhancement algorithm based on Gaussian mixture model. The problem is that the estimation algorithm underflows during training. XI am trying to calculate the product of the PDF of each frequnecy component of the Gaussian cluster gi

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