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For the purpose of DBSCAN clustering, the points are classified as core points, (directly-) reachable points and outliers, as follows: A point p is a core point if at least minPts points are within distance ε of it (including p). A point q is directly reachable from p if point q is within distance ε from core point p. Points are only said to ...
English: Illustration of en:DBSCAN cluster analysis (minPts=3). Points around A are core points. Points B and C are not core points, but are density-connected via the cluster of A (and thus belong to this cluster). Point N is Noise, since it is neither a core point nor reachable from a core point.
A point p is a core point if at least MinPts points are found within its ε-neighborhood () (including point p itself). In contrast to DBSCAN , OPTICS also considers points that are part of a more densely packed cluster, so each point is assigned a core distance that describes the distance to the MinPts th closest point:
Objects that belong to the k nearest neighbors of B (the "core" of B, see DBSCAN cluster analysis) are considered to be equally distant. The reason for this is to reduce the statistical fluctuations between all points A close to B, where increasing the value for k increases the smoothing effect. [1]
Another interesting property of DBSCAN is that its complexity is fairly low – it requires a linear number of range queries on the database – and that it will discover essentially the same results (it is deterministic for core and noise points, but not for border points) in each run, therefore there is no need to run it multiple times.
A cluster in DBSCAN is only guaranteed to consists of at least 1 core point. Since border points that belong to more than 1 cluster will be "randomly" (usually: first-come) assigned to one of the clusters, a core point may not be able to retain/get all its neighbors. Thus, it may be smaller than minPts. One dimensional example: minPts=4, epsilon=1:
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The average silhouette of the data is another useful criterion for assessing the natural number of clusters. The silhouette of a data instance is a measure of how closely it is matched to data within its cluster and how loosely it is matched to data of the neighboring cluster, i.e., the cluster whose average distance from the datum is lowest. [8]