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  Cluster Identification in Nearest-Neighbor Graphs

Maier, M., Hein, M., & von Luxburg, U. (2007). Cluster Identification in Nearest-Neighbor Graphs. In M. Hutter, R. Servedio, & E. Takimoto (Eds.), Algorithmic Learning Theory: 18th International Conference, ALT 2007, Sendai, Japan, October 1-4, 2007 (pp. 196-210). Berlin, Germany: Springer.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-0013-CB8F-B Version Permalink: https://hdl.handle.net/21.11116/0000-0003-D1AF-C
Genre: Conference Paper

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https://link.springer.com/content/pdf/10.1007%2F978-3-540-75225-7_18.pdf (Publisher version)
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 Creators:
Maier, M1, 2, Author           
Hein, M1, 2, 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: Assume we are given a sample of points from some underlying distribution which contains several distinct clusters. Our goal is
to construct a neighborhood graph on the sample points such that
clusters are ``identifiedamp;lsquo;amp;lsquo;: that is, the subgraph induced by points
from the same cluster is connected, while subgraphs corresponding to
different clusters are not connected to each other. We derive bounds
on the probability that cluster identification is successful, and
use them to predict ``optimalamp;lsquo;amp;lsquo; values of k for the mutual and
symmetric k-nearest-neighbor graphs. We point out different
properties of the mutual and symmetric nearest-neighbor graphs
related to the cluster identification problem.

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 Dates: 2007-10
 Publication Status: Issued
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: -
 Identifiers: DOI: 10.1007/978-3-540-75225-7_18
BibTex Citekey: 4590
 Degree: -

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Title: 18th International Conference on Algorithmic Learning Theory (ALT 2007)
Place of Event: Sendai, Japan
Start-/End Date: 2007-10-01 - 2007-10-04

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Title: Algorithmic Learning Theory: 18th International Conference, ALT 2007, Sendai, Japan, October 1-4, 2007
Source Genre: Proceedings
 Creator(s):
Hutter, M, Editor
Servedio, RA, Editor
Takimoto, E, Editor
Affiliations:
-
Publ. Info: Berlin, Germany : Springer
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: 196 - 210 Identifier: ISBN: 978-3-540-75224-0

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Title: Lecture Notes in Computer Science
Source Genre: Series
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Publ. Info: -
Pages: - Volume / Issue: 4754 Sequence Number: - Start / End Page: - Identifier: -