Fuzzy clustering for categorical multivariate data

This paper proposes a new fuzzy clustering algorithm for categorical multivariate data. The conventional fuzzy clustering algorithms form fuzzy clusters so as to minimize the total distance from cluster centers to data points. However, they cannot be applied to the case where only cooccurrence relations among individuals and categories are given and the criterion to obtain clusters is not available. The proposed method enables us to handle that kind of data set by maximizing the degree of aggregation among clusters. The clustering results by the proposed method show similarity to those of correspondence analysis or Hayashi's (1952) quantification method Type III. Numerical examples show the usefulness of our method.