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/}
}