Adaptive Clustering Using Kernel Density Estimators
Machine Learning
2021-11-02 v3 Methodology
Abstract
We derive and analyze a generic, recursive algorithm for estimating all splits in a finite cluster tree as well as the corresponding clusters. We further investigate statistical properties of this generic clustering algorithm when it receives level set estimates from a kernel density estimator. In particular, we derive finite sample guarantees, consistency, rates of convergence, and an adaptive data-driven strategy for choosing the kernel bandwidth. For these results we do not need continuity assumptions on the density such as H\"{o}lder continuity, but only require intuitive geometric assumptions of non-parametric nature.
Cite
@article{arxiv.1708.05254,
title = {Adaptive Clustering Using Kernel Density Estimators},
author = {Ingo Steinwart and Bharath K. Sriperumbudur and Philipp Thomann},
journal= {arXiv preprint arXiv:1708.05254},
year = {2021}
}