Introduction
Like k-means, a Gaussian mixture needs to know how many clusters to look for. For k-means we used inertia and silhouette scores, but those assume round clusters, so they're unreliable for the elliptical, overlapping clusters that GMMs model.
Because a GMM is a probability model, we can use more principled tools:
- Information criteria (AIC and BIC) — scores that reward fitting the data well but penalise complexity.
- Bayesian Gaussian mixtures — models that automatically switch off clusters they don't need.