The k-modes method using possibility and rough set theories

Abstract

This paper investigates rough clustering of objects from uncertain databases using possibility and rough set theories. Real databases can contain both certain and uncertain attribute values. To properly cluster such instances into different clusters, it is necessary to take into account such uncertainty. When clustering objects with uncertain values, we have to consider the similarities between each object and all clusters in order to provide more accurate clustering results. To this end, we propose a new approach based on the k-modes method to cluster categorical objects using possibility and rough set theories to deal with uncertainty. First, possibility theory is applied to handle uncertain attribute values of instances and to specify membership degrees of each instance to all clusters. Then, rough set theory is used to detect peripheral objects and to form clusters with rough boundaries. The results of the proposed approach compare favourably with other certain and uncertain approaches based on different evaluation criteria.