Gaussian Mixture Models Tool

Visualize and understand Gaussian Mixture Models (GMM) for clustering, density estimation, and the Expectation-Maximization algorithm.

What are Gaussian Mixture Models?

Gaussian Mixture Models (GMM) are probabilistic models that assume data is generated from a mixture of several Gaussian distributions with unknown parameters. They're used for clustering, density estimation, and as a flexible alternative to k-means that provides probability estimates for cluster membership.

Data Input & Generation

Enter Your Data (x,y coordinates, one per line):

Three Clusters

Circular Pattern

Linear Pattern

Random Scatter

GMM Configuration

Model Parameters

Number of Components:

Max EM Iterations:

Covariance Type: Full Tied Diagonal Spherical

Visualization

Show Cluster Assignments

Show Gaussian Ellipses

Show Probability Surfaces

Show Component Centroids

EM Algorithm

Initialize with K-Means

Initialize Randomly

Show EM Steps

GMM Visualization

Generating visualization...

Gaussian Mixture Model Fit

Component 1

Component 2

Component 3

Component 4

EM Algorithm Steps

Expectation-Maximization Algorithm

1

Initialization

Initialize Gaussian component parameters (means, covariances, mixing coefficients) randomly or using k-means.

2

Expectation Step (E-Step)

Calculate the probability that each data point belongs to each Gaussian component using current parameter estimates.

3

Maximization Step (M-Step)

Update Gaussian component parameters (means, covariances, mixing coefficients) to maximize the expected log-likelihood.

4

Convergence Check

Check if the log-likelihood has converged (changes less than tolerance) or if max iterations reached.

5

Final Assignment

Assign each data point to the Gaussian component with the highest probability (hard assignment) or keep soft probabilities.

Model Results & Analysis

Model Parameters

Probabilities

Performance

GMM Component Parameters

Each Gaussian component is defined by its mean (center), covariance matrix (shape/orientation), and mixing coefficient (weight).

Component 1

Weight (π): 0.35

Mean (μ): [2.1, 3.4]

Covariance (Σ): [[0.8, 0.1], [0.1, 0.6]]

Component Membership Probabilities

Each data point has a probability of belonging to each Gaussian component (soft clustering). Values are between 0 and 1.

Data Point	Component 1	Component 2	Component 3	Assigned To

Model Performance Metrics

Log-Likelihood

Measure of how well the model fits the data:

-142.3

Bayesian Information Criterion (BIC)

Model selection criterion (lower is better):

312.6

Convergence Iterations

EM iterations until convergence:

12

Silhouette Score

Cluster quality measure (-1 to 1):

0.68

Understanding GMM Performance

Log-Likelihood: Higher values indicate better fit to the data.
BIC: Penalizes model complexity; used to select optimal number of components.
Silhouette Score: Measures how similar points are to their own cluster vs other clusters.
Convergence: EM algorithm typically converges in 10-50 iterations.

How to Add This GMM Tool to Your Blogger Site

Step 1: Copy All Code

Select all the code on this page (click and drag or press Ctrl+A then Ctrl+C). The entire page is a single HTML file.

Step 2: Create New Blog Post

In your Blogger dashboard, create a new post or edit an existing one where you want to add the tool.

Step 3: Switch to HTML Mode

Click the "HTML" button in the post editor to switch from Compose to HTML mode.

Step 4: Paste & Publish

Paste the copied code (Ctrl+V) into the HTML editor, then publish or update your post.

Where Are Gaussian Mixture Models Used?

GMMs are widely used in: Clustering (flexible alternative to k-means), Density Estimation (approximating complex distributions), Anomaly Detection (identifying outliers), Image Segmentation (separating foreground/background), Speech Recognition (modeling phoneme distributions), Financial Modeling (asset return distributions), and Bioinformatics (gene expression analysis).

Gaussian Mixture Models Visualization Tool | Designed for Blogger | No Coding Knowledge Required

Probabilistic Clustering & Expectation-Maximization Algorithm