Gaussian mixture model--maximum likelihood

    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?

Answer 1

[Walter Roberson]

I would suggest reading the File Exchange contribution http://www.mathworks.com/matlabcentral/fileexchange/18785

[i Venky]

Which method is best suitable for voice recognition?

[i Venky]

I tried that file and it didn't work.

[Walter Roberson]

What happened when you tried that file?

I never make a statement about which technique is "best" for something. There are always other techniques that I haven't heard of, or perhaps which have not been invented yet, or which might happen to be faster or more accurate for your *particular* situation even if they are provably less accurate in general. The concept of "best" means different things to different people. For example, you probably would not think very much of a technique that could promise 100% accuracy but took 17.89 million years to execute.

Answer 2

[i Venky]

 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.

Answer 3

[i Venky]

Someone please answer my question.

[Walter Roberson]

My team of substitute sleepers get Sunday evening off, so I have to do the sleeping myself.

[i Venky]

Okay. After a long time I am coming back here. What's the answer?

[Jan]

@i Venky: Walter asked: "What happened when you tried that file?"

Answer 4

[Walter Roberson]

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.