Machine Learning
Clustering Metrics
A clustering has no answer key to be marked against, so every score has to decide what it is comparing with. Silhouette, Davies–Bouldin and DBCV look only at the geometry. Purity, the Rand index and its adjusted form compare with the true classes, and they disagree with each other in instructive ways.
colour is the cluster foundshape is the true classwhat the metric rewardswhat it counts against
Scroll to zoom, drag to pan, double-click to reset the view · hover a point to follow it through the metric · click a point to move it to the next cluster
Silhouette—
—
Explain
Data
Clusters from
clusters found—
points—
pairs of points—
outvoted in their cluster—
What to observe
- On Moons, switch between k-means and True classes. Silhouette and DBI prefer the straight k-means cut, because they measure distance to a centre; DBCV follows chains of dense points and prefers the crescents.
- DBSCAN on Circles finds both rings exactly, so purity, Rand and ARI are perfect, yet silhouette sits near 0. Only DBCV, built on the same idea of density, gives it credit.
- Purity on Uneven climbs to 1 as k grows, because cutting a cluster into pieces never makes a piece less uniform. Inverse purity is the one that falls.
- With Random clusters the Rand index still reads 0.5 or more, since pairs apart in both agree for free. ARI rescales so random labels land at 0, which is why it is the one to report.
Shortcuts:r reset · f fullscreen