Abstract
Cluster collections obtained within the framework of most cluster structures studied in data analysis and classification are essentially Moore families. In this paper, we propose a simple intuitive necessary and sufficient condition for some subset of objects to be a critical set of a finite Moore family. This condition is based on a new characterization of quasi-closed sets. Moreover, we provide a necessary condition for a subset containing more than k objects (k ≥ 2) to be a critical set of a k-weakly hierarchical Moore family. Finally, as a consequence of this result, we identify critical sets of some k-weakly hierarchical Moore families and thereby generalize a result earlier obtained by Domenach and Leclerc in the particular case of weak hierarchies.
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Diatta, J. On critical sets of a finite Moore family. Adv Data Anal Classif 3, 291–304 (2009). https://doi.org/10.1007/s11634-009-0053-8
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DOI: https://doi.org/10.1007/s11634-009-0053-8