# Modal clustering asymptotics with applications to bandwidth selection

## TL;DR

This paper investigates the asymptotic properties of density estimation in modal clustering, focusing on bandwidth selection to accurately identify clusters based on density modes.

## Contribution

It introduces an asymptotic framework for density estimation in modal clustering and proposes a method for bandwidth selection based on this theory.

## Key findings

- Asymptotic approximation of the partition distance metric
- Guidelines for bandwidth selection in modal clustering
- Improved understanding of density estimation impact on clustering accuracy

## Abstract

Density-based clustering relies on the idea of linking groups to some specific features of the probability distribution underlying the data. The reference to a true, yet unknown, population structure allows to frame the clustering problem in a standard inferential setting, where the concept of ideal population clustering is defined as the partition induced by the true density function. The nonparametric formulation of this approach, known as modal clustering, draws a correspondence between the groups and the domains of attraction of the density modes. Operationally, a nonparametric density estimate is required and a proper selection of the amount of smoothing, governing the shape of the density and hence possibly the modal structure, is crucial to identify the final partition. In this work, we address the issue of density estimation for modal clustering from an asymptotic perspective. A natural and easy to interpret metric to measure the distance between density-based partitions is discussed, its asymptotic approximation explored, and employed to study the problem of bandwidth selection for nonparametric modal clustering.