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

Fuzzy c-means clustering and its derivatives are very successful on many clustering problems. However, fuzzy c-means clustering and similar algorithms have problems with high dimensional data sets and a large number of prototypes. In particular, we discuss hard c-means, noise clustering, fuzzy c-means with a polynomial fuzzifier function and its noise variant. A special test data set that is optimal for clustering is used to show weaknesses of said clustering algorithms in high dimensions. We also show that a high number of prototypes influences the clustering procedure in a similar way as a high number of dimensions. Finally, we show that the negative effects of high dimensional data sets can be reduced by adjusting the parameter of the algorithms, i.e. the fuzzifier, depending on the number of dimensions.