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Sequential clustering with radius and split criteria

  • Nenad Mladenovic
  • Pierre Hansen
  • Jack Brimberg
Original Paper

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.

Keywords

Clustering Sequential Efficient cluster Radius Split 

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Nenad Mladenovic
    • 1
  • Pierre Hansen
    • 2
  • Jack Brimberg
    • 3
  1. 1.Brunel UniversityLondonUK
  2. 2.GERADHEC MontrealMontrealCanada
  3. 3.Royal Military CollegeKingstonCanada

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