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Generalized hard cluster analysis

Wim De Mulder (UGent)
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Abstract
In this paper, we generalize the hard clustering paradigm. While in this paradigm a data set is subdivided into disjoint clusters, we allow different clusters to have a nonempty intersection. The concept of hard clustering is then analysed in this general setting, and we show which specific properties hard clusterings possess in comparison to more general clusterings. We also introduce the concept of equivalent clusterings and show that in the case of hard clusterings equivalence and equality coincide. However, if more general clusterings are considered, these two concepts differ, and this implies the undesired fact that equivalent clusterings can have different representations in the traditional view on clustering. We show how a matrix representation can solve this representation problem.
Keywords
matrix representation, transitivity, (m, n)-set, hard clustering, equivalent clusterings

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MLA
De Mulder, Wim. “Generalized Hard Cluster Analysis.” INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, vol. 88, no. 12, 2011, pp. 2516–26, doi:10.1080/00207160.2011.560667.
APA
De Mulder, W. (2011). Generalized hard cluster analysis. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 88(12), 2516–2526. https://doi.org/10.1080/00207160.2011.560667
Chicago author-date
De Mulder, Wim. 2011. “Generalized Hard Cluster Analysis.” INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 88 (12): 2516–26. https://doi.org/10.1080/00207160.2011.560667.
Chicago author-date (all authors)
De Mulder, Wim. 2011. “Generalized Hard Cluster Analysis.” INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 88 (12): 2516–2526. doi:10.1080/00207160.2011.560667.
Vancouver
1.
De Mulder W. Generalized hard cluster analysis. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS. 2011;88(12):2516–26.
IEEE
[1]
W. De Mulder, “Generalized hard cluster analysis,” INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, vol. 88, no. 12, pp. 2516–2526, 2011.
@article{3067724,
  abstract     = {{In this paper, we generalize the hard clustering paradigm. While in this paradigm a data set is subdivided into disjoint clusters, we allow different clusters to have a nonempty intersection. The concept of hard clustering is then analysed in this general setting, and we show which specific properties hard clusterings possess in comparison to more general clusterings. We also introduce the concept of equivalent clusterings and show that in the case of hard clusterings equivalence and equality coincide. However, if more general clusterings are considered, these two concepts differ, and this implies the undesired fact that equivalent clusterings can have different representations in the traditional view on clustering. We show how a matrix representation can solve this representation problem.}},
  author       = {{De Mulder, Wim}},
  issn         = {{0020-7160}},
  journal      = {{INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS}},
  keywords     = {{matrix representation,transitivity,(m,n)-set,hard clustering,equivalent clusterings}},
  language     = {{eng}},
  number       = {{12}},
  pages        = {{2516--2526}},
  title        = {{Generalized hard cluster analysis}},
  url          = {{http://doi.org/10.1080/00207160.2011.560667}},
  volume       = {{88}},
  year         = {{2011}},
}

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