Gaussian Mixture Models
Gaussian Mixture Models related concepts are explained in the notebook below. Please practice and ask your questions in the forum if any. Please don’t share the notebook anywhere without our permission.
Table of Contents
Gaussian Mixture Models: Concept And Application
Gaussian Mixture Model (GMM) vs. K-Means:
Comparison
| Comparison | K-Means | GMM |
|---|---|---|
| Objective | Partition data into K clusters with nearest mean | Model data as a mixture of Gaussian distributions |
| Cluster Shape | Spherical and equally sized clusters | Flexible, accommodates varied shapes and sizes |
| Uncertainty and Probabilistic Assignment | Provides hard assignments | Provides probabilistic assignments (soft clustering) |
| Assumption | Assumes equal variance and isotropic clusters | Allows for different variances and covariances |
| Initialization Sensitivity | Sensitive to initial centroid placement | Less sensitive to initialization |
Advantages and Disadvantages:
K-Means:
| Aspect | Advantages | Disadvantages |
|---|---|---|
| Overview | Simple and computationally efficient | Sensitive to outliers |
| Cluster Shape | Works well for well-separated, spherical clusters | Assumes clusters are of similar size and shape |
| Scalability | Scalable to large datasets | Limited to linear cluster boundaries |
GMM:
| Aspect | Advantages | Disadvantages |
|---|---|---|
| Flexibility | More flexible in accommodating varied cluster shapes and sizes | Computationally more intensive than K-Means |
| Uncertainty | Provides uncertainty measures through probabilistic assignments | May converge to a local minimum, sensitive to initialization |
| Overlapping Clusters | Can model overlapping clusters | Requires estimating more parameters |
When to Use Which:
| Scenario | K-Means | GMM |
|---|---|---|
| Cluster Shape Assumption | Isotropic, equally sized clusters | Different shapes or sizes are present |
| Computational Efficiency | Simple and computationally efficient | Tolerant to higher computational cost |
| Cluster Assignments | Hard cluster assignments are sufficient | Soft (probabilistic) cluster assignments are desired |
