I have 3 classes and I modeled the GMM for those classes with 12 components for each model.
Now I have a data from one of the 3 classes. I want to find out the class that the data belongs to. I tried finding out the likelihood but I don't know how to proceed next to make the decision.
I have about 12 likelihood values for each class. What should I do next?
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I would suggest reading http://www.mathworks.com/help/toolbox/stats/bq_679x-24.html#bra9fvn or looking at the File Exchange contribution http://www.mathworks.com/matlabcentral/fileexchange/18785
I have only one doubt. I have about 12 means for every class and when I compare it with the given data (and find the log likelihood) I get about 12 values for every class. If it was only one value for a class then I would just find the maximum value but here I have about 12 values so I got confused.
What you should do is apply a distance function to find the "distance" between any given sample and the centroids of the 3 classes. The class with the lowest distance has the greatest probability of being the class the sample is a member of.
A simple distance function is Euclidean distance. It is not used that much in classification questions: instead more common is to use a metric that takes in to account the covariance matrices. For example, using the Anderson-Bahadur metric is common.