Stability of Density-Based Clustering
Abstract
High density clusters can be characterized by the connected components of a level set L(λ) = x: p(x)>λ of the underlying probability density function p generating the data, at some appropriate level λ ≥ 0. The complete hierarchical clustering can be characterized by a cluster tree T= ∪λL(λ). In this paper, we study the behavior of a density level set estimate L̂(λ) and cluster tree estimate T̂ based on a kernel density estimator with kernel bandwidth h. We define two notions of instability to measure the variability of L̂(λ) and T̂ as a function of h, and investigate the theoretical properties of these instability measures.
Cite
Text
Rinaldo et al. "Stability of Density-Based Clustering." Journal of Machine Learning Research, 2012.Markdown
[Rinaldo et al. "Stability of Density-Based Clustering." Journal of Machine Learning Research, 2012.](https://mlanthology.org/jmlr/2012/rinaldo2012jmlr-stability/)BibTeX
@article{rinaldo2012jmlr-stability,
title = {{Stability of Density-Based Clustering}},
author = {Rinaldo, Alessandro and Singh, Aarti and Nugent, Rebecca and Wasserman, Larry},
journal = {Journal of Machine Learning Research},
year = {2012},
pages = {905-948},
volume = {13},
url = {https://mlanthology.org/jmlr/2012/rinaldo2012jmlr-stability/}
}