Unsupervised Learning: Clustering #3

DBSCAN / HDBSCAN

  • Density-based Clustering
  • HDBSCAN

Best for: Arbitrary-shaped clusters, noise detection Aliases: Density-based Clustering, HDBSCAN

How it works

$$\mathrm{core}(p)\iff |\{q:\mathrm{dist}(p,q)\le\varepsilon\}|\ge \mathrm{min\_pts}$$

DBSCAN defines clusters as maximal sets of density-reachable points: a point is a core point when at least min_pts neighbours lie within radius $\varepsilon$, points reachable through chains of core points join the same cluster, and everything else is labelled noise. This yields arbitrary-shaped clusters and automatic noise labels without specifying $k$. HDBSCAN extends this to varying density via the mutual-reachability distance $d_{\mathrm{mreach}}(a,b)=\max\{\mathrm{core}_k(a),\mathrm{core}_k(b),d(a,b)\}$, building a hierarchy and extracting the most stable clusters across it.

When to use

Arbitrary-shaped clusters with noise; cases where you don’t want to pre-specify k; geospatial and anomaly work.

Watch out

Struggles with varying cluster density (DBSCAN); eps and min_samples tuning matter; HDBSCAN is slower but more robust.

Common fields

Geospatial data · anomaly detection · fraud · network analysis