Analysis of a Mode Clustering Diagram

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.