DBSCAN(Density-based spatial clustering of applications with noise)

Density-based spatial clustering of applications with noise (DBSCAN) is a data clustering algorithm proposed by Martin Ester, Hans-Peter Kriegel, Jörg Sander and Xiaowei Xu in 1996.[1] It is a density-based clustering algorithm: given a set of points in some space, it groups together points that are closely packed together (points with many nearby neighbors), marking as outliers points that lie alone in low-density regions (whose nearest neighbors are too far away). DBSCAN is one of the most common clustering algorithms and also most cited in scientific literature.[2]

In 2014, the algorithm was awarded the test of time award (an award given to algorithms which have received substantial attention in theory and practice) at the leading data mining conference, KDD.[3]

Contents
1 Preliminary
2 Algorithm
3 Complexity
4 Advantages
5 Disadvantages
6 Parameter estimation
7 Extensions
8 Availability
9 See also
10 Notes
11 References
11.1 Further readin

Preliminary

Consider a set of points in some space to be clustered. For the purpose of DBSCAN clustering, the points are classified as core points, (density-)reachable points and outliers, as follows:

A point p is a core point if at least minPts points are within distance ε(ε is the maximum radius of the neighborhood from p) of it (including p). Those points are said to be directly reachable from p. By definition, no points are directly reachable from a non-core point.
A point q is reachable from p if there is a path p1, ..., pn with p1 = p and pn = q, where each pi+1 is directly reachable from pi (all the points on the path must be core points, with the possible exception of q).
All points not reachable from any other point are outliers.
Now if p is a core point, then it forms a cluster together with all points (core or non-core) that are reachable from it. Each cluster contains at least one core point; non-core points can be part of a cluster, but they form its "edge", since they cannot be used to reach more points.

wiki: https://en.wikipedia.org/wiki/DBSCAN