Fuzzy clustering with outliers

In this paper we introduce a modified objective function for fuzzy clustering. We add an additional weighting factor for each datum and derive necessary conditions for the introduced parameter in order to optimise the objective function. These conditions are used in an alternating optimisation scheme to calculate a partition of sample data. The obtained weights determine a kind of representativeness of each datum for the data distribution. They can be used to identify outliers and enable the expert to locate critical areas that are often represented by only a few outliers.