# Density-Based Clustering

**DOI:**https://doi.org/10.1007/978-1-4614-8265-9_605

## Definition

Density-based clusters are dense areas in the data space separated from each other by sparser areas. Furthermore, the density within the areas of noise is lower than the density in any of the clusters. Formalizing this intuition, for each *core point* the neighborhood of radius *Eps* has to contain at least *MinPts* points, i.e., the density in the neighborhood has to exceed some threshold. A point *q* is *directly-density-reachable* from a core point *p* if *q* is within the Eps-neighborhood of *p*, and *density-reachability* is given by the transitive closure of direct density-reachability. Two points *p* and *q* are called *density-connected* if there is a third point *o* from which both *p* and *q* are density-reachable. A *cluster* is then a set of density-connected points which is maximal with respect to density-reachability. *Noise*is defined as the set of points in the database not belonging to any of its clusters. The task of density-based clustering is to find all clusters with respect to...

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