Fuzzy Cluster Validation Using the Partition Negentropy Criterion

Abstract

Esta es la versión de autor del congreso publicado en: This is an author produced version of a paper published in: 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.

Evaluation of Negentropy-Based Cluster Validation Techniques in Problems With Increasing Dimensionality

“…New experiments with other databases are required in order to check if this property is general. We expect that this finding will be more accentuated in benchmarks with non Gaussian clusters (Biernacki et al, 2000;Lago-Fernández et al, 2009). This will be the subject of future work.…”