# Fully adaptive density-based clustering

arXiv: https://arxiv.org/abs/1409.8437 · HTML: https://mlsanity.com/paper/1409.8437/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Sep 2014.

## Built on by (most cited first, 4 of 4)

- [Moving Up the Cluster Tree with the Gradient Flow](https://mlsanity.com/paper/2109.08362/) (2021)
- [An Asymptotic Equivalence between the Mean-Shift Algorithm and the Cluster Tree](https://mlsanity.com/paper/2111.10298/) (2021)
- [Bagged k-Distance for Mode-Based Clustering Using the Probability of Localized Level Sets](https://mlsanity.com/paper/2210.09786/) (2022)
- [Model-free Estimation of Latent Structure via Multiscale Nonparametric Maximum Likelihood](https://mlsanity.com/paper/2410.22248/) (2024)

## Abstract (arXiv)

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.