Machine Learning Algorithms - Second Edition

Finding the optimal number of components

When the desired number of components is not known or there are no specific constraints, it's necessary to evaluate different models in order to decide which configuration is the best. As Gaussian mixture is a model based on the maximization of likelihood, a helpful method is provided by the Akaike Information Criterion (AIC). Let's suppose that the total number of parameters is n_p (of course, we are not considering the hyperparameters, but only the means, covariances, and weights) and that the maximum log-likelihood achieved after fitting the model is L_opt. If this is the case, then the AIC is defined as follows:

As it considers the negative log-likelihood, the smaller the AIC is, the higher the ...