TY - JOUR
TI - On the number of clusterings in a hierarchical classication model with overlapping clusters
AU - Roman, Adam
AU - Podolak, Igor T.
AU - Deszyńska, Agnieszka
TI - On the number of clusterings in a hierarchical classication model with overlapping clusters
AB - 
	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.
VL - 2011
IS - Volume 20
PY - 2012
SN - 1732-3916
C1 - 2083-8476
SP - 137
EP - 159
DO - 10.4467/20838476SI.11.007.0293
UR - https://ejournals.eu/en/journal/schedae-informaticae/article/on-the-number-of-clusterings-in-a-hierarchical-classication-model-with-overlapping-clusters