On the number of clusterings in a hierarchical classication model with overlapping clusters
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Publication date: 23.01.2012
Schedae Informaticae, 2011, Volume 20, pp. 137 - 159
https://doi.org/10.4467/20838476SI.11.007.0293Authors
On the number of clusterings in a hierarchical classication model with overlapping clusters
This paper shows a new combinatorial problem which emerged from studies on an artificial intelligence classification model of a hierarchical classifier. 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.
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Information: Schedae Informaticae, 2011, Volume 20, pp. 137 - 159
Article type: Original article
Titles:
On the number of clusterings in a hierarchical classication model with overlapping clusters
On the number of clusterings in a hierarchical classication model with overlapping clusters
Faculty of Mathematics and Computer Science, Jagiellonian University, Krakow, Poland
Faculty of Mathematics and Computer Science, Jagiellonian University, Krakow, Poland
Faculty of Mathematics and Computer Science, Jagiellonian University, Cracow, Poland
Published at: 23.01.2012
Article status: Open
Licence: None
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