  Mode-based clustering methods define clusters to be the basins of attraction
of the modes of a density estimate. The most common version is mean shift clus-
tering which uses a gradient ascent algorithm to find the basins. Rodriguez and
Laio (2014) introduced a new method that is faster and simpler than mean shift
clustering. Furthermore, they define a clustering diagram that provides a sim-
ple, two-dimensional summary of the mode clustering information. We study the
statistical properties of this diagram and we propose some improvements and
extensions. In particular, we show a connection between the diagram and robust
linear regression.
