Fully adaptive density-based clustering

TL;DR

This paper introduces a fully adaptive density-based clustering algorithm that estimates the critical density level and connected components without user-specified parameters, with proven consistency and convergence rates.

Contribution

It proposes a generic, adaptive algorithm for density-based clustering that automatically determines the relevant density level and estimator parameters.

Findings

Finite sample analysis of the algorithm

Consistent estimation of density level and components

Rates of convergence for estimation accuracy

Abstract

The clusters of a distribution are often defined by the connected components of a density level set. However, this definition depends on the user-specified level. We address this issue by proposing a simple, generic algorithm, which uses an almost arbitrary level set estimator to estimate the smallest level at which there are more than one connected components. In the case where this algorithm is fed with histogram-based level set estimates, we provide a finite sample analysis, which is then used to show that the algorithm consistently estimates both the smallest level and the corresponding connected components. We further establish rates of convergence for the two estimation problems, and last but not least, we present a simple, yet adaptive strategy for determining the width-parameter of the involved density estimator in a data-depending way.