Before class read em.pdf and in class we are going to find a GMM for the Cmaj chord based on chroma data from the Beatles dataset.
 
1) Write an EM algorithm which finds k number of mixtures for 12 dimensional chroma data
       use chroma.mat data (thanks Annie!). It is a 12xN matrix which will be used as the training data for our GMM. It is comprised of all the frames in the Beatles dataset which correspond to Cmaj
 
2) you can use gmDistribution.m as a starting template for your EM function. I've commented all the necessary steps.
 
3) Sanity Check: for debugging/development purposes it might be easier to start with the smaller 2-dimensional old faithful dataset from the chapter external link: oldFaithful.mat
 
       - My results using a hardcoded initialization and after the first iteration are in this file external link: sanityCheck.txt
       - The joint probability densities and posteriors probabilities after the first iteration can be found in these files
         jointPD.mat
        posterior.mat