Cluster Definition in DBSCAN

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[Core Point: A point is a core point if at least minPts of points exist within a radius of epsilon centered at that point.

[Directly Reachable: If point p is a core point and point q is within distance ε of p, then q is considered directly reachable from p.

Reachable: If there is a sequence of consecutive directly reachable points from point p to point q, then q is considered reachable from p.

[Density-Connected: Points p and q are density-connected if they are reachable from each other via some point o.

Based on these concepts, DBSCAN defines clusters as follows

Cluster: the largest set of points for which all points are density-connected to each other and from which any point in the cluster can be reached from any other point.

Noise point: not belonging to any cluster.

Thus, DBSCAN defines clusters based on data density and identifies noise points.

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