Problems of Fuzzy c-Means Clustering and Similar Algorithms with High Dimensional Data Sets

Abstract

Fuzzy c-Means and its derivatives work very well on most clustering problems. However, FcM and many similar algorithms have their problems with high dimensional data sets and a large number of prototypes. Similar algorithms in this context are those, which generate fuzzy membership values by using a ratio of distances to ensure a sum of membership values of 1. Possibilistic clustering is explicitly of no concern because the degrees of possibility are computed for each cluster individually. In this paper, we exploit some structural problems using the ratio of distances as normalisation method in high dimensional spaces. We also show that a high number of prototypes influences the clustering procedure in a similar way as a high number of dimensions. Both effects are not entirely independent since the number of dimensions can be effectively reduced if the number of prototypes is smaller than the number of dimensions.