A modified Fuzzy k-Partition based on indiscernibility relation for categorical data clustering

Abstract

Categorical data clustering has been adopted by many scientific communities to classify objects from large databases. In order to classify the objects, Fuzzy k-Partition approach has been proposed for categorical data clustering. However, existing Fuzzy k-Partition approaches suffer from high computational time and low clustering accuracy. Moreover, the parameter maximize of the classification likelihood function in Fuzzy k-Partition approach will always have the same categories, hence producing the same results. To overcome these issues, we propose a modified Fuzzy k-Partition based on indiscernibility relation. The indiscernibility relation induces an approximation space which is constructed by equivalence classes of indiscernible objects, thus it can be applied to classify categorical data. The novelty of the proposed approach is that unlike previous approach that use the likelihood function of multivariate multinomial distributions, the proposed approach is based on indescernibility relation. We performed an extensive theoretical analysis of the proposed approach to show its effectiveness in achieving lower computational complexity. Further, we compared the proposed approach with Fuzzy Centroid and Fuzzy k-Partition approaches in terms of response time and clustering accuracy on several UCI benchmark and real world datasets. The results show that the proposed approach achieves lower response time and higher clustering accuracy as compared to other Fuzzy k-based approaches.