Please use this identifier to cite or link to this item:
https://hdl.handle.net/2440/75412
Type: | Journal article |
Title: | Characterization, stability and convergence of hierarchical clustering algorithms |
Author: | Carlsson, Gunnar Memoli, Facundo |
Citation: | Journal of Machine Learning Research, 2010; 11(4):1425-1470 |
Publisher: | MIT Press |
Issue Date: | 2010 |
ISSN: | 1532-4435 |
School/Discipline: | School of Computer Science |
Statement of Responsibility: | clustering; hierarchical clustering; stability of clustering; Gromov-Hausdorff distance |
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. |
Rights: | © 2010 Gunnar Carlsson and Facundo Mémoli |
Published version: | http://jmlr.csail.mit.edu/papers/v11/carlsson10a.html |
Appears in Collections: | Computer Science publications |
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