reachabilityplot

A reachability plot is a visualization used in density-based clustering, most commonly with the OPTICS algorithm. It displays the reachability distance of each point in the order produced by OPTICS, plotted against the point’s position in that order. The plot provides a compact representation of the clustering structure in a dataset without imposing a fixed global density threshold.

Construction and definition: During the OPTICS process, each point has a core distance, defined as the distance to its minPts-th nearest neighbor. The reachability distance of a point i with respect to a predecessor j is defined as the maximum of the core distance of j and the actual distance between i and j. The reachability plot uses, for each point in the OPTICS order, its reachability distance as the y-value and the order index as the x-value. The result is a waveform-like curve that summarizes local density variations along the order.

Interpretation: In a reachability plot, clusters are typically represented by valleys—continuous runs of low reachability distances—while large peaks or gaps indicate transitions between clusters or sparsely populated regions. Deeper valleys correspond to denser clusters, and the location of valleys helps identify cluster boundaries. Clusters can be extracted by thresholding the plot or by identifying significant drops from peaks.

Limitations and usage: The interpretation of a reachability plot depends on parameter choices, such as minPts (and sometimes epsilon). The plot provides a qualitative view of the clustering structure and often requires manual or semi-automatic analysis to delineate clusters. It is a central tool in OPTICS-based clustering but can be complemented by quantitative criteria for final cluster extraction.