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I am using a Hidden Markov Model with Gaussian mixture emissions to cluster a sequential data (I am using hmmlearn in python 3). Initially, I used the log likelihood to find the number of clusters and gaussian mixtures, however, this value kept increasing as the complexity of the model grew (the number of states and mixtures increased); AIC did the same (decreased, at the same parameters). So I decided to use SSE (sum of squared errors, or the squared distance of each sample to the centroid of the state), which had the least value for 13 states, 3 mixtures. However, when I checked this model, there were empty states,i.e., none of my training samples was classified in those states. These empty states seemed to have the same parameters as other non empty states (same values in the transition matrix). Should I just discard the empty states and modify the transition matrix by adding the probabilities of equivalent states?

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