OPTICS Reachability Plot

Question

I can't seem to visualize how the reachability distances of objects are arranged in the Reachability Plot of OPTICS. So how do "valleys" form in reachability plots? It says in the original paper that the visualization is independent of the dimension of the data set. It also says something about the cluster order on the horizontal axis and the epsilon on the vertical axis. How do they arrange the reachability distances anyway to form valleys? The set of objects and their corresponding reachability distances?

Answer 1

OPTICS processes elements in a particular order. This order is used for the X axis.

ELKI includes a working implementation of OPTICS, and it will also visualize the cluster order using a reachability plot.

This image on Wikimedia (unfortunately not yet used in the english OPTICS article), was generated using ELKI except for the three dashed colored lines mapping the clusters to valleys.