Fuzzy Cluster Validation Using the Partition Negentropy Criterion

Authors:
Luis F. Lago-Fernández;Manuel Sánchez-Montañés;Fernando Corbacho
Affiliations:
Departamento de Ingeniería Informática, Escuela Politécnica Superior, Universidad Autónoma de Madrid, Madrid, Spain 28049;Departamento de Ingeniería Informática, Escuela Politécnica Superior, Universidad Autónoma de Madrid, Madrid, Spain 28049;Cognodata Consulting, Madrid, Spain 28010
Venue:
ICANN '09 Proceedings of the 19th International Conference on Artificial Neural Networks: Part II
Year:
2009

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Abstract

We introduce the Partition Negentropy Criterion (PNC) for cluster validation. It is a cluster validity index that rewards the average normality of the clusters, measured by means of the negentropy, and penalizes the overlap, measured by the partition entropy. The PNC is aimed at finding well separated clusters whose shape is approximately Gaussian. We use the new index to validate fuzzy partitions in a set of synthetic clustering problems, and compare the results to those obtained by the AIC, BIC and ICL criteria. The partitions are obtained by fitting a Gaussian Mixture Model to the data using the EM algorithm. We show that, when the real clusters are normally distributed, all the criteria are able to correctly assess the number of components, with AIC and BIC allowing a higher cluster overlap. However, when the real cluster distributions are not Gaussian (i.e. the distribution assumed by the mixture model) the PNC outperforms the other indices, being able to correctly evaluate the number of clusters while the other criteria (specially AIC and BIC) tend to overestimate it.