GMM

Gaussian Mixture Model & Expectation Maximization

AI, ML, Stats
AI, ML, Stats, GMM, Expectation Maximization, Clustering

Gaussian Mixture Model & Expectation Maximization #

A Gaussian Mixture Model represents data as a weighted combination of multiple Gaussian distributions.

It is commonly used for soft clustering and density estimation.

Key takeaway:
K-means gives hard cluster membership.

GMM gives probabilities of belonging to each cluster.

  • Gaussian Mixture Model
  • soft clustering
  • mixing coefficients
  • latent variables
  • likelihood and log-likelihood
  • Expectation-Maximization algorithm
  • E-step and M-step
  • responsibilities
  • convergence

Motivation ☆ #

Many real datasets are not described well by one Gaussian distribution.

Unsupervised Learning

AI, ML
AI, ML, Unsupervised Learning, K-Means, EM, GMM, Clustering

Unsupervised Learning #

Unsupervised Learning is used when we have input data but no target labels.

The model is not told the correct answer. Instead, it tries to discover hidden structure in the data.

  • K-means Clustering and variants
  • Review of EM algorithm
  • GMM based Soft Clustering
  • Applications

Supervised vs Unsupervised Learning #

AspectSupervised LearningUnsupervised Learning
Data contains target label?YesNo
Learns fromInput-output pairsInput features only
Main goalPredict outputDiscover structure
Example taskClassification, regressionClustering
Example algorithmLogistic regression, decision treeK-means, GMM
  • Works on unlabelled raw data.
  • The algorithm discovers hidden patterns without prior knowledge of outcomes.
  • Requires no human intervention during training.
  • Does not make direct predictions — it groups or organises data instead.
  • Carries a higher risk because there’s no ground truth to verify results.
  • Common techniques include Clustering, Association, and Dimensionality Reduction.

The most common example is clustering, where similar records are grouped together.