What are some options for identifying the number of components in a GMM?

When used for clustering, any of the evaluation metrics discussed previously (Silhouette Score, Dunn Index, Rand Index, etc.) are appropriate for evaluating the quality of clusters produced by a GMM. However, since GMM seeks to estimate the underlying densities of multiple normal distributions, the quality of the fit of the densities can also be evaluated using the Likelihood or AIC/BIC.