There are two primary methods for selecting the optimal number of components in a Gaussian Mixture Model (GMM): 1. Information Criteria: Utilizing metrics like the Bayesian Information Criterion (BIC) to balance model fit against complexity. 2. Split Test (Cross-Validation): Evaluating the model's performance on a validation set across varying numbers of components. The optimal number is typically chosen at the "elbow" or "knee" point of the performance curve.