- Unsupervised Learning
-
Overview
- Introduction to Unsupervised Learning
- K-Means Clustering Algorithm
- Hierarchical Clustering
- Principal Component Analysis (PCA)
- Autoencoders for Dimensionality Reduction
- Gaussian Mixture Models (GMM)
- Association Rule Learning (Apriori, FP-Growth)
- DBSCAN Clustering Algorithm
- Self-Organizing Maps (SOM)
- Applications of Unsupervised Learning
Gaussian Mixture Models (GMM)
Add to BookmarkGaussian Mixture Models (GMM) are a probabilistic approach to clustering based on the assumption that data points are generated from a mixture of several Gaussian distributions. Unlike K-Means, GMMs provide soft clustering — meaning each data point belongs to multiple clusters with certain probabilities.
GMMs are especially useful when:
- Clusters overlap
- Data is not spherical
- We want probabilistic assignment rather than hard labels
How GMM Works
A GMM models data as a mixture of multiple multivariate Gaussian distributions. Each Gaussian is defined by:
- Mean (μ): Center of the distribution
- Covariance (Σ): Shape/orientation
- Weight (π): Proportion of that component in the mixture
The model estimates parameters using the Expectation-Maximization (EM) algorithm:
- E-Step: Estimate the probability that each point belongs to each Gaussian component
- M-Step: Update the parameters (μ, Σ, π) to maximize the likelihood
Key Features of GMM
Feature | Description |
---|---|
Type | Probabilistic model |
Clustering style | Soft (fuzzy) clustering |
Distribution | Mixture of Gaussians |
Suitable for | Non-spherical, overlapping, probabilistic data |
Output | Probability of each point in each cluster |
Python Example Using sklearn
from sklearn.mixture import GaussianMixture
from sklearn.datasets import make_blobs
import matplotlib.pyplot as plt
import numpy as np
# Generate synthetic data
X, y_true = make_blobs(n_samples=300, centers=3, cluster_std=1.0, random_state=42)
# Fit GMM
gmm = GaussianMixture(n_components=3, random_state=42)
gmm.fit(X)
# Predict cluster probabilities and labels
probs = gmm.predict_proba(X)
labels = gmm.predict(X)
# Visualize results
plt.figure(figsize=(8, 5))
plt.scatter(X[:, 0], X[:, 1], c=labels, s=40, cmap='viridis')
plt.title("Gaussian Mixture Model Clustering")
plt.xlabel("Feature 1")
plt.ylabel("Feature 2")
plt.grid(True)
plt.show()
Output-
Explanation
make_blobs
: Generates synthetic data with clear clustersGaussianMixture
: Trains GMM on datapredict
: Assigns most likely clusterpredict_proba
: Gives probabilities of cluster memberships
Applications of GMM
- Customer segmentation
- Speaker identification
- Image segmentation
- Anomaly detection
- Financial modeling (market regimes)
Advantages of GMM
- Soft clustering (probabilities) gives richer information
- Can model elliptical clusters (not just spherical like K-Means)
- Flexible: can vary number of components, covariance structure
- Works well even when clusters overlap
Limitations of GMM
- Sensitive to initialization and number of components
- Assumes data is normally distributed
- EM can get stuck in local optima
- More computationally expensive than K-Means
Tips for Beginners
- Start with visualizable 2D data to understand clustering behavior
- Use
AIC
andBIC
to choose the optimal number of components - Standardize input data before applying GMM
Tips for Professionals
- Try different
covariance_type
values (full
,tied
,diag
,spherical
) - Use GMM for semi-supervised learning when partial labels are available
- Combine GMM with PCA or t-SNE for high-dimensional clustering
- Use GMM as a base for anomaly detection (low-probability samples)
Summary
Gaussian Mixture Models provide a flexible, probabilistic way to perform clustering. They go beyond hard assignments by modeling overlapping clusters using Gaussian distributions. GMMs are a great choice for tasks where clusters are not clearly separated or when you need confidence scores for predictions.
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