Characterization, Stability and Convergence of Hierarchical Clustering Methods
Abstract
We study hierarchical clustering schemes under an axiomatic view. We show that within this framework, one can prove a theorem analogous to one of Kleinberg (2002), in which one obtains an existence and uniqueness theorem instead of a non-existence result. We explore further properties of this unique scheme: stability and convergence are established. We represent dendrograms as ultrametric spaces and use tools from metric geometry, namely the Gromov-Hausdorff distance, to quantify the degree to which perturbations in the input metric space affect the result of hierarchical methods.
Cite
Text
Carlsson and Mémoli. "Characterization, Stability and Convergence of Hierarchical Clustering Methods." Journal of Machine Learning Research, 2010.Markdown
[Carlsson and Mémoli. "Characterization, Stability and Convergence of Hierarchical Clustering Methods." Journal of Machine Learning Research, 2010.](https://mlanthology.org/jmlr/2010/carlsson2010jmlr-characterization/)BibTeX
@article{carlsson2010jmlr-characterization,
title = {{Characterization, Stability and Convergence of Hierarchical Clustering Methods}},
author = {Carlsson, Gunnar and Mémoli, Facundo},
journal = {Journal of Machine Learning Research},
year = {2010},
pages = {1425-1470},
volume = {11},
url = {https://mlanthology.org/jmlr/2010/carlsson2010jmlr-characterization/}
}