Analysis of a Mode Clustering Diagram

TL;DR

This paper investigates the statistical properties of a mode clustering diagram introduced by Rodriguez and Laio, proposing improvements and establishing a connection to robust linear regression, enhancing understanding and application of mode-based clustering methods.

Contribution

The paper analyzes the properties of the mode clustering diagram, introduces improvements, and links it to robust linear regression, advancing mode clustering techniques.

Findings

The clustering diagram's statistical properties are characterized.

Proposed extensions improve the diagram's interpretability.

A novel connection to robust linear regression is established.

Abstract

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.