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  Relating clustering stability to properties of cluster boundaries

Ben-David, S., & von Luxburg, U. (2008). Relating clustering stability to properties of cluster boundaries. In R. Servedio, & T. Zhang (Eds.), 21st Annual Conference on Learning Theory (COLT 2008) (pp. 379-390). Madison, WI, USA: Omnipress.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-0013-C83F-8 Version Permalink: https://hdl.handle.net/21.11116/0000-0003-3D87-1
Genre: Conference Paper

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 Creators:
Ben-David, S, Author
von Luxburg, U1, 2, Author           
Affiliations:
1Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society, ou_1497795              
2Max Planck Institute for Biological Cybernetics, Max Planck Society, Spemannstrasse 38, 72076 Tübingen, DE, ou_1497794              

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 Abstract: In this paper, we investigate stability-based methods
for cluster model selection, in particular to select
the number K of clusters. The scenario under
consideration is that clustering is performed
by minimizing a certain clustering quality function,
and that a unique global minimizer exists. On
the one hand we show that stability can be upper
bounded by certain properties of the optimal clustering,
namely by the mass in a small tube around
the cluster boundaries. On the other hand, we provide
counterexamples which show that a reverse
statement is not true in general. Finally, we give
some examples and arguments why, from a theoretic
point of view, using clustering stability in a
high sample setting can be problematic. It can be
seen that distribution-free guarantees bounding the
difference between the finite sample stability and
the “true stability” cannot exist, unless one makes
strong assumptions on the underlying distribution.

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 Dates: 2008-07
 Publication Status: Issued
 Pages: -
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 Table of Contents: -
 Rev. Type: -
 Identifiers: BibTex Citekey: 5105
 Degree: -

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Title: 21st Annual Conference on Learning Theory (COLT 2008)
Place of Event: Helsinki, Finland
Start-/End Date: 2008-07-09 - 2008-07-12

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Title: 21st Annual Conference on Learning Theory (COLT 2008)
Source Genre: Proceedings
 Creator(s):
Servedio, RA, Editor
Zhang, T, Editor
Affiliations:
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Publ. Info: Madison, WI, USA : Omnipress
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 379 - 390 Identifier: ISBN: 978-1-60558-205-4