Core / border / noise
Core point: ≥ minPts within ε. Border: within ε of core but not core itself. Noise: neither.
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Algorithm
For each unvisited point: if core, expand cluster via BFS through density-reachable points. Others → noise.
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Complexity
O(N² ) naive. O(N log N) with spatial index (k-d tree). Suffers curse of dimensionality above ~10 dims.
HDBSCAN
Hierarchical DBSCAN. Extracts flat clusters via hierarchy. Only requires min_cluster_size. Modern default.