OPTICS algorithm

Ordering points to identify the clustering structure (OPTICS) is an algorithm for finding density-basedclusters in spatial data. It was presented by Mihael Ankerst, Markus M. Breunig, Hans-Peter Kriegel and Jörg Sander. Its basic idea is similar to DBSCAN, but it addresses one of DBSCAN's major weaknesses: the problem of detecting meaningful clusters in data of varying density. In order to do so, the points of the database are (linearly) ordered such that points which are spatially closest become neighbors in the ordering. Additionally, a special distance is stored for each point that represents the density that needs to be accepted for a cluster in order to have both points belong to the same cluster. This is represented as a dendrogram.

Like DBSCAN, OPTICS requires two parameters: ${\displaystyle \varepsilon }$, which describes the maximum distance (radius) to consider, and ${\displaystyle MinPts}$, describing the number of points required to form a cluster. A point ${\displaystyle p}$ is a core point if at least ${\displaystyle MinPts}$ points are found within its ${\displaystyle \varepsilon }$-neighborhood ${\displaystyle N_{\varepsilon }(p)}$. Contrary to DBSCAN, OPTICS also considers points that are part of a more densely packed cluster, so each point is assigned a core distance that describes the distance to the ${\displaystyle MinPts}$th closest point:

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