My question is similar to this question Clustering with shape prior, but with additional information.
The second answer suggests a mixture model approach to this problem, which is something like Expectation Maximization with user-defined mixture model for clusters instead of default Gaussian.My question is that suppose we have an additional optimization criteria with respect to clustering (for e.g. the total area of the clusters should be minimum), where can this point be introduced in the approach. Is proper similarity measure the only way to ensure the desired optimization ? If yes, Which part of EM algorithm can be modified to take this into account, I mean which part in EM algorithm emulates the function of distance metric in k-means. And is there any implementation of EM that let's us specify the mixture model. Is expectation-maximization the only way to achieve this model based clustering ? Any references would be very helpful.