Figuring out absolute probability in GMM training.

[geneus]

Trying to classify sounds based on MFCCs and a few other features. I'm using the GMM example as the base for my program. (.ipp_samplespeech-recSpeech-ProcessingGMM_Training)

When I classify a sound as belonging to one class or another, all I get are the log likelihood probability ratios, using which I can determine the class. However, what I need is to display the probability of a sound belonging to the class from 0 to 100, since the log-likelihood ratio is a meaningless number as far as a user is concerned%.

Any suggestions from the guys above?

[Intel_C_Intel]

To get %s you can call ippsLogSum function to get the log of sum of likelihoods. Then exp of the differencebetween thelogsum and each of log likelihood multiplied by 100 is the required %

[geneus]

Thank you, this was very helpful, although not exactly what I wanted to achieve...



In the sample code referred to in the original post, the Log likelihood ratios were found for different GMMs using the same input vector and then compared. Your post describes how to combine those Log likelihood ratios into percentages so that the probability of all of the GMMs add up to 100%. Now, perhaps I don't exactly understand the theory behind this, but when I get the Log likelihood ratio, isn't it an absolute measure of how similar the input vector is to the mixture described by the GMM?



What I mean is, is it possible from the LogLH ratio to get an absolute measure of similarity between the input vector and the model? Some sort of mapping between the LogLH ratios and probability, so that, for example, always the LogLH ratio of -48.5 means that the vector is 85% similar to the GMM, and the LogLH ratio of -53.124 means the input vector is 47% similar.



The way the relative probability percentages work as you described in your answer, even if the classifier receives an input vector that it was not explicitly trained to recognize, the sum of its probabilities will always be 100%, and even though the sound does not fit any one of the GMMs, there's a high chance that the GMM that is most similar to the input vector will provide a very high probability of a match. I am looking for a way to eliminate these false positives.



I hope I explained this well enough.



Thank you very much for your help!

Message Edited by genEus on 10-31-2005 08:05 AM

[Intel_C_Intel]

Log likelihoods are really logarithms of probabilities.

The comparison of log likelihoods can give you only relative measure of proximity of recognised object to patterns. To determine absolute proximity you need to use some additional algorithms. Eg some kind of heuristic estimation of likelihood per frame. This task is tricky and depends on many things. Silence in detected speech has similar proximity for all patterns. Likelihood of different speech fragments of the same speaker can differ substantially. But generally, some rude estimation of the absolute proximity can be done using the average value of it.

[geneus]

Thanks again for your reply.

I think I need to understand better how the Log Likelihood is actually calculated, so, can you tell me the source where you got the formula for the LogGaussMixture function?

Thanks

[Intel_C_Intel]

Log likelihood is the natural logarithm of the probability (likelihood). LogGauss family functions caclulate the logarithm of the Gaussian mixture or its components. The formuli are in IPP manual (Sygnal Processing, Chapter 8 Speech Recognition Functions)

[geneus]

Sorry, I saw the formula in the IPP manual but I was looking for the actual reference book from where that formula was taken so that I could go back to it and figure out how the Gaussian mixture model works. Thanks again!

Message Edited by genEus on 11-03-2005 01:02 PM