2019-01-11[Stay Sharp]DBSCAN

what is DBSCAN ?

DBSCAN stands for Density-based spatial clustering of applications with noise, it's a density-based clustering algorithm. It groups together points in high-density regions, and marks points in low-density regions as outliers. DBSCAN is one of the most common clustering algorithms and also most cited in scientific literature.

how does DBSCAN work?

dbscan is an algorithm with parameters of .
Before we describe how dbscan works, there are some terms we need to know at first.

• core point. core point is the point that has at least points are within the distance .
• directly reachable. directly reachable point is the one which is within distance from a core point.
• reachable. reachable point is the one that can be connected to a core point by a path, and each point on the path is directly reachable to the neighbor point.
• not reachable. a point that is not reachable to any other point, it's an outlier.
• density-connected. two points and are density-connected when there exists a point such that both and are reachable to the point.

image.png

In the above picture, the is 4, all red points such as A are core points because each point has 4 points around(including itself) within the distance of which is the radius of the red circle. B and C are not core points, but they are reachable to A. N is not reachable.

so, let's take a step back, what kind of points can be clustered as a cluster: any point is reachable from any other point of the cluster.
All points in the cluster are mutaully density-connected.

References

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