Robust fuzzy classification

One of the most important problems among the methodological issues discussed in cluster analysis is the identification of the correct number of clusters and the correct allocation of units to their natural clusters. The most widely used index to determine the optimal number of groups is the Calinski Harabasz index. As shown in this paper, the presence of atypical observations has a strong effect on this index and may lead to the determination of a wrong number of groups. Furthermore, in order to study the degree of belonging of each unit to each group it is standard practice to apply a fuzzy k-means algorithm. In this paper we tackle this problem using a robust and efficient approach based on a forward search algorithm. The method is applied on a data set containing performance evaluation indicators of Italian universities.