DBSCAN^{1} is a very popular density-based clustering algorithm. The main idea is to detect clusters in a similar way as we perceive structure: the density of data points \(\fvec{p}_i\) is higher inside the cluster than outside of it. DBSCAN links these points together allowing it to detect arbitrarily shaped clusters. For this, each point defines a neighbourhood

which is used to search for other points so that the links can be created. Since \eqref{eq:DBSCAN_Neighbourhood} uses the Euclidean distance, the neighbourhood is defined by a circle with radius \(\varepsilon\) around a point \(\fvec{p}_i\) in the dataset. This is visualized in the following figure for a small two-dimensional example.

List of attached files:

- DBSCAN.nb [PDF] (Mathematica notebook used to create the basic visualization (as SVG file) which is later animated with JavaScript)

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