DBSCAN

Synopsis

This operator performs clustering with DBSCAN. DBSCAN (for density-based spatial clustering of applications with noise) is a density-based clustering algorithm because it finds a number of clusters starting from the estimated density distribution of corresponding nodes.

Description

DBSCAN's definition of a cluster is based on the notion of density reachability. Basically, a pointqis directly density-reachable from a pointpif it is not farther away than a given distance epsilon (i.e. it is part of its epsilon-neighborhood) and ifpis surrounded by sufficiently many points such that one may considerpandq是集群的一部分。qis called density-reachable (note the distinction from "directly density-reachable") frompif there is a sequencep(1),…,p(n)of points withp(1) = pandp(n) = q其中每个p(i+1)is directly density-reachable fromp(i).

Note that the relation of density-reachable is not symmetric.qmight lie on the edge of a cluster, having insufficiently many neighbors to count as dense itself. This would halt the process of finding a path that stops with the first non-dense point. By contrast, starting the process withqwould lead top(though the process would halt there,pbeing the first non-dense point). Due to this asymmetry, the notion of density-connected is introduced: two pointspandqare density-connected if there is a pointosuch that bothpandqare density-reachable fromo. Density-connectedness is symmetric.

A cluster, which is a subset of the points of the data set, satisfies two properties:

1. All points within the cluster are mutually density-connected.
2. If a point is density-connected to any point of the cluster, it is part of the cluster as well.

DBSCAN requires two parameters: epsilon and the minimum number of points required to form a cluster (minimal_points). epsilon and minPts can be specified through theepsilonandmin pointsparameters respectively. DBSCAN starts with an arbitrary starting point that has not been visited. This point's epsilon-neighborhood is retrieved, and if it contains sufficiently many points, a cluster is started. Otherwise, the point is labeled as noise. Note that this point might later be found in a sufficiently sized epsilon-environment of a different point and hence be made part of a cluster.

If a point is found to be a dense part of a cluster, its epsilon-neighborhood is also part of that cluster. Hence, all points that are found within the epsilon-neighborhood are added, as is their own epsilon-neighborhood when they are also dense. This process continues until the density-connected cluster is completely found. Then, a new unvisited point is retrieved and processed, leading to the discovery of a further cluster or noise.

This operator also creates scores for the assignments. Scores are the minimal distances to a member of the respective cluster.

In the application phase the algorithm checks if there are at least minPoints of a given cluster in it's epsilon neighbourhood. If so, the data point is assigned to the given cluster. If there is no cluster which fulfills the condition, the cluster assignment is 'Noise'. If there is more than one cluster which fulfills the condition, then the cluster which has the minimal point to point distance is chosen. This is the minimum distance to any data point in the given cluster.

Input

example set

This input port expects an ExampleSet. It is output of the Retrieve operator in the attached Example Process.

Output

example set

The resulting data set with the cluster assignments.

original

The original data set passed through.

model

This port delivers the cluster model. It has information regarding the clustering performed. It tells which examples are part of which cluster.

Parameters

Epsilon

This parameter specifies the epsilon parameter of the DBSCAN algorithm. epsilon specifies the size of the neighborhood.

Minimal points

This parameter specifies the minimal number of points which needs to be in the epsilon neighborhood to call a point part of the cluster.