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Dynamic programming and convex clustering

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Abstract

In this paper the notion of convexity of clusterings for the given ordering of units is introduced. In the case when at least one (optimal) solution of the clustering problem is convex, dynamic programming leads to a polynomial algorithm with complexityO(kn 3). We prove that, for several criterion functions, convex optimal clusterings exist when dissimilarity is pyramidal for a given ordering of units.

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Authors and Affiliations

  1. Department of Mathematics, University of Ljubljana, Jadranska 19, 61111, Ljubljana, Slovenia

    Vladimir Batagelj & Simona Korenjak-Černe

  2. Pedagoška fakulteta Maribor, University of Maribor, Koroška c. 160, 62000, Maribor, Slovenia

    Sandi Klavžar

Authors
  1. Vladimir Batagelj
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  2. Simona Korenjak-Černe
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  3. Sandi Klavžar
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Additional information

Communicated by Jean-Daniel Boissonnat.

This research was supported in part by the Research Council of Slovenia.

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Batagelj, V., Korenjak-Černe, S. & Klavžar, S. Dynamic programming and convex clustering. Algorithmica 11, 93–103 (1994). https://doi.org/10.1007/BF01182769

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  • DOI: https://doi.org/10.1007/BF01182769

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