Machine Learning
Gaussian Mixtures
k-means hands every point to one cluster and draws only circles. A mixture of Gaussians gives every point a share of each cluster instead, and lets a cluster be stretched and tilted, so a point sitting between two of them is finally allowed to say so.
each ellipse is one componenta point shared between clustersthe likelihood, which only ever rises
Hover a point to see how the clusters divide it · run to fit, step for one round of EM
Log-likelihood per point—
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Data
Shape allowed
log-likelihood per point—
rounds of EM—
mixing weights—
points genuinely shared—
What to observe
- Each Step is one round of EM: move and reshape the ellipses given the shares, then divide every point between them again. A point between two clusters comes out a mixed colour, the doubtk-means throws away.
- On Stretched with shape Any each ellipse lies along its stripe. Set the shape to Round and the circles cannot follow, so the likelihood per point settles lower.
- Same circle plus equal weights plus one cluster each is k-means exactly: every point goes to its nearest centre, and each centre moves to the mean of its points.
- Ask for more components than the data has. The likelihood still rises, so it cannot tell you how many clusters there really are.
Shortcuts:space run/pause · s step · r reset · f fullscreen