Effects of Irrelevant Attributes in Fuzzy Clustering

In fuzzy clustering soft cluster partitions are formed based on the similarity of data points to the respective cluster prototypes. Similarity is defined in terms of simultaneous closeness regarding all attributes. In some applications the values of many attributes have been measured, but a natural clustering, if it exists, occurs within a (small) subset of attributes. The remaining dimensions can be considered irrelevant. They can obscure an existing grouping and make it harder to discover the cluster structure. In probabilistic fuzzy clustering irrelevant attributes can lead to coincidental cluster centers in the worst case. We study this effect in detail as well as the robustness of different similarity functions and their possible parameterizations against irrelevant input dimensions. Empirical evidence is given for the different properties of the membership functions