Gaussian Mixture Model

Probabilistic model that assumes data comes from a mixture of Gaussian distributions with unknown parameters.

When to use:

• Want probabilistic cluster assignments
• Clusters have elliptical shapes
• Need uncertainty estimates
• Have normally distributed data

Strengths: Soft clustering (probabilities), flexible cluster shapes (elliptical), model selection with BIC/AIC, handles overlapping clusters Weaknesses: Assumes Gaussian distribution, sensitive to initialization, can overfit with too many components

Model Parameters

N Components (default: 1, required) Number of Gaussian components (clusters). Similar to k in K-Means.

• Use BIC/AIC scores to select optimal number
• Too few: Underfits complex data
• Too many: Overfits, finds spurious clusters

Covariance Type (default: "full") Shape of covariance matrices:

• full: Each component has its own covariance matrix (most flexible)
• tied: All components share same covariance (assumes similar shapes)
• diag: Diagonal covariance (axis-aligned ellipses, faster)
• spherical: Single variance per component (similar to K-Means)

Tolerance (default: 0.001) Convergence threshold. Lower values = more iterations.

• 0.001-0.01: Standard
• <0.001: Stricter convergence

Max Iterations (default: 100) Maximum EM iterations to perform.

• 100: Usually sufficient
• 200+: For difficult convergence

Random State (default: 42) Seed for reproducibility.