What are some options for identifying the number of components in a GMM?
When used for clustering, any of the evaluation metrics (Silhouette Score, Dunn Index, Rand Index, etc.) are appropriate
silhouette score
What is Silhouette Score?
Silhouette Score compares the distance of observations to the centroids of the clusters they are assigned to against that to the centroids of other clusters in an algorithm like K-Means.