FORMULATIONS OF FUZZY CLUSTERING FOR CATEGORICAL DATA

Abstract

New formulations of the fuzzy clustering algorithm for categorical data are proposed in this paper. Although fuzzy c-means algorithm usually uses distances from cluster centers, the distances of the memberships weighted with categorical data from the unit vectors are used in our new formulations. Different types of metrics between the weighted membership vectors and unit vectors are considered for the objective functions. Optimal solutions for the objective functions are derived and illustrative examples are given to show the obtained theoretic results.