Faster DBScan and HDBScan in Low-Dimensional Euclidean Spaces

We present a new algorithm for the widely used density-based clustering method dbscan. Our algorithm computes the dbscan-clustering in O(n log n) time in R, irrespective of the scale parameter ε (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 ε than the original dbscan algorithm. We also present an O(n log n) 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.