Centroid-based clustering can struggle with irregularly shaped clusters and explicit noise points. DBSCAN instead defines clusters as connected dense regions.

Choose a neighborhood radius $\varepsilon$ and minimum neighbor count minPts.

• A core point has at least minPts points in its $\varepsilon$-neighborhood.
• Points reachable through chains of neighboring core points belong to the same cluster.
• Nearby non-core points can be border points.
• Points not density-reachable from any core region are labeled noise.

Imagine points sampled around two curved crescents plus a few isolated outliers. A centroid-based partition tends to divide space into compact regions, while DBSCAN can follow each crescent and leave isolated points unclustered.

The method does not require specifying the number of clusters in advance, but it does require a meaningful distance and density scale. A single global $\varepsilon$ can perform poorly when different clusters have very different densities.

Feature scaling matters because the neighborhood geometry is distance based. DBSCAN's key inductive bias is therefore not “clusters have centroids” but “clusters are connected regions of sufficiently high local density.”