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Galois closed entity sets and k-balls of quasi-ultrametric multi-way dissimilarities

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Abstract

Quasi-ultrametric multi-way dissimilarities and their respective sets of k-balls extend the fundamental bijection in classification between ultrametric pairwise dissimilarities and indexed hierarchies. We show that nonempty Galois closed subsets of a finite entity set coincide with k-balls of some quasi-ultrametric multi-way dissimilarity. This result relates the order theoretic Galois connection based clustering approach to the dissimilarity based one. Moreover, it provides an effective way to specify easy-to-interpret cluster systems, from complex data sets, as well as to derive informative attribute implications.

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  1. IREMIA, Université de la Réunion, 15 avenue René Cassin, BP 7151, 97715, Saint-Denis messag cedex 9, France

    Jean Diatta

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  1. Jean Diatta
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Correspondence to Jean Diatta.

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Diatta, J. Galois closed entity sets and k-balls of quasi-ultrametric multi-way dissimilarities. ADAC 1, 53–65 (2007). https://doi.org/10.1007/s11634-006-0005-5

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