▶Component distributions
Each Gaussian describes one local pattern in the data, with its own center and spread.
Gaussian Mixture Distributions
Building complex distributions from simple components
A Gaussian mixture combines several Gaussian components using nonnegative weights that sum to one. Simple pieces can therefore represent clusters, skewness, or multiple peaks.
watchone idea
→manipulateone example
→leave withone intuition
The essential idea: a complicated density can be assembled from a small number of interpretable Gaussian components.
One Concept · One Example
What to notice
- Each component has its own mean and variance.
- Mixing weights control component prevalence.
- Membership can be probabilistic, not just hard labels.
A model with two layers
Mixture distribution
The full density adds the weighted component densities at every possible value of x.
When do two groups become two visible peaks?
Adjust the separation, common spread, and mixing weight. Then probe one value to see its soft component assignment.
mixturecomponent 1component 2
Gaussian mixtures turn simple Gaussian components into flexible, interpretable models of clustered and multimodal data.