On the number of clusterings in a hierarchical classi cation model with overlapping clusters

Bibliographic description

punktacja MEiN [2011 B]: 6

title:	On the number of clusterings in a hierarchical classi cation model with overlapping clusters
author:	Roman Adam , Podolak Igor , Deszyńska Agnieszka
journal title:	Schedae Informaticae
volume:	20
date of publication :	2011
pages:	137-157
ISSN:	1732-3916
eISSN:	2083-8476
language:	English
journal language:	English
abstract in English:	This paper shows a new combinatorial problem which emerged from studies on an arti cial intelligence classi cation model of a hierarchical classi er. We introduce the notion of proper clustering and show how to count their number in a special case when 3 clusters are allowed. An algorithm that generates all clusterings is given. We also show that the proposed approach can be generalized to any number of clusters, and can be automatized. Finally, we show the relationship between the problem of counting clusterings and the Dedekind problem.
affiliation:	Wydział Matematyki i Informatyki : Instytut Informatyki i Matematyki Komputerowej
type:	journal article
subtype:	academic paper