I am reading about the EM (Expectation-Maximization) algorithm in a machine learning book. At the end remark of the chapter, the authors mentioned that we cannot decide the optimality of the number of components (# of mixtures of Gaussians distributions) based on each model's log likelihood at the end--since models with more parameters will inevitably describe the data better. Therefore, my questions are 1) How do we compare the performance of each model using a different number of components?2) What are the important factors that help us to decide that an EM model is sufficient for modeling the observed data? 
How to compare the performance of different number of mixing components for EM algorithm?
machine learning;data mining;clustering;expectation maximization