# Density-based Clustering with Best-scored Random Forest

## TL;DR

This paper introduces a novel density-based clustering algorithm called 'best-scored clustering forest' that selects the best-performing random tree to determine optimal clusters, with proven consistency and competitive accuracy.

## Contribution

It proposes a new ensemble clustering method that guarantees consistency and convergence, improving upon existing density-based clustering techniques.

## Key findings

- Algorithm achieves high accuracy on synthetic data
- Demonstrates competitive performance on real benchmark datasets
- Proven theoretical guarantees of consistency and convergence

## Abstract

Single-level density-based approach has long been widely acknowledged to be a conceptually and mathematically convincing clustering method. In this paper, we propose an algorithm called "best-scored clustering forest" that can obtain the optimal level and determine corresponding clusters. The terminology "best-scored" means to select one random tree with the best empirical performance out of a certain number of purely random tree candidates. From the theoretical perspective, we first show that consistency of our proposed algorithm can be guaranteed. Moreover, under certain mild restrictions on the underlying density functions and target clusters, even fast convergence rates can be achieved. Last but not least, comparisons with other state-of-the-art clustering methods in the numerical experiments demonstrate accuracy of our algorithm on both synthetic data and several benchmark real data sets.