Generalized fuzzy c-means clustering in the presence of outlying data

Some data sets contain outlying data values which can degrade the quality of the clustering results obtained using standard techniques such as the fuzzy c-means algorithm. This note gives an extended family of fuzzy c-means type models, and attempts to empirically identify those members of the family which are least influenced by the presence of outliers. The form of the extended family of clustering criteria suggests an alternating optimization approach is feasible, and specific algorithms for implementing the optimization of the models are stated. The implemented approach is then tested using various artificial data sets.