A fuzzy k-partitions model for categorical data and its comparison to the GoM model

The grade of membership (GoM) model uses fuzzy sets as memberships of each individual to extreme profiles (or classes) on the likelihood function of multivariate multinomial distributions. The GoM clustering algorithm derived from the GoM model is used in cluster analysis for categorical data, but it is iterated with complicated calculations. In this paper we create another approach, termed a fuzzy k-partitions (FkP) model, which is also based on the likelihood function of multivariate multinomial distributions. However, the calculations of the FkP algorithm for clustering categorical data derived from the proposed FkP model are simpler. The proposed FkP clustering algorithm is not only easier in calculation than the GoM, but also has more accuracy and computation efficiency. To verify it, we employ real empirical data and also some simulation data. We find that FkP has superior results to GoM. We then apply these two algorithms to classification of pathology. The results show the superiority of the FkP clustering algorithm. Moreover, the proposed FkP algorithm can be used as a fuzzy clustering algorithm for categorical data. Some comparisons between FkP and two popular algorithms, fuzzy k-modes and fuzzy centroids, are made. These results show that the FkP clustering algorithm can be another useful tool in analyzing categorical data.