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Sequential clustering with radius and split criteria

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  • Nenad Mladenovic
  • Pierre Hansen
  • Jack Brimberg

Abstract

Sequential clustering aims at determining homogeneous and/or well-separated clusters within a given set of entities, one at a time, until no more such clusters can be found. We consider a bi-criterion sequential clustering problem in which the radius of a cluster (or maximum dissimilarity between an entity chosen as center and any other entity of the cluster) is chosen as a homogeneity criterion and the split of a cluster (or minimum dissimilarity between an entity in the cluster and one outside of it) is chosen as a separation criterion. An O(N 3 ) algorithm is proposed for determining radii and splits of all efficient clusters, which leads to an O(N 4 ) algorithm for bi-criterion sequential clustering with radius and split as criteria. This algorithm is illustrated on the well known Ruspini data set. Copyright Springer-Verlag 2013

Suggested Citation

  • Nenad Mladenovic & Pierre Hansen & Jack Brimberg, 2013. "Sequential clustering with radius and split criteria," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(1), pages 95-115, June.
    • Handle: RePEc:spr:cejnor:v:21:y:2013:i:1:p:95-115
    DOI: 10.1007/s10100-012-0258-3
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    References listed on IDEAS

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    3. J. C. Gower & G. J. S. Ross, 1969. "Minimum Spanning Trees and Single Linkage Cluster Analysis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 18(1), pages 54-64, March.
    4. B. Mirkin, 1987. "Additive clustering and qualitative factor analysis methods for similarity matrices," Journal of Classification, Springer;The Classification Society, vol. 4(1), pages 7-31, March.
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    Cited by:

    1. Andrej Kastrin & Janez Povh & Lidija Zadnik Stirn & Janez Žerovnik, 2021. "Methodologies and applications for resilient global development from the aspect of SDI-SOR special issues of CJOR," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(3), pages 773-790, September.
    2. Tibor Csendes & Lidija Zadnik Stirn & Janez Žerovnik, 2013. "Editorial," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(1), pages 1-2, June.

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