Faster DBSCAN and HDBSCAN in Low-Dimensional Euclidean Spaces

Abstract

We present a new algorithm for the widely used density-based clustering method dbscan. For a set of [Formula: see text] points in [Formula: see text] our algorithm computes the dbscan-clustering in [Formula: see text] time, irrespective of the scale parameter [Formula: see text] (and assuming the second parameter MinPts is set to a fixed constant, as is the case in practice). Experiments show that the new algorithm is not only fast in theory, but that a slightly simplified version is competitive in practice and much less sensitive to the choice of [Formula: see text] than the original dbscan algorithm. We also present an [Formula: see text] randomized algorithm for hdbscan in the plane — hdbscan is a hierarchical version of dbscan introduced recently — and we show how to compute an approximate version of hdbscan in near-linear time in any fixed dimension.