Hierarchical Quasi-Clustering Methods for Asymmetric Networks
Abstract
This paper introduces hierarchical quasi-clustering methods, a generalization of hierarchical clustering for asymmetric networks where the output structure preserves the asymmetry of the input data. We show that this output structure is equivalent to a finite quasi-ultrametric space and study admissibility with respect to two desirable properties. We prove that a modified version of single linkage is the only admissible quasi-clustering method. Moreover, we show stability of the proposed method and we establish invariance properties fulfilled by it. Algorithms are further developed and the value of quasi-clustering analysis is illustrated with a study of internal migration within United States.
Keywords
Cite
@article{arxiv.1404.4655,
title = {Hierarchical Quasi-Clustering Methods for Asymmetric Networks},
author = {Gunnar Carlsson and Facundo Mémoli and Alejandro Ribeiro and Santiago Segarra},
journal= {arXiv preprint arXiv:1404.4655},
year = {2014}
}
Comments
Accepted to the 31st International Conference on Machine Learning (ICML), Beijing, China, 2014