Fuzzy cluster analysis from the viewpoint of robust statistics

Abstract

Fuzzy cluster analysis has been initiated in the beginning of the seventies by Bezdek [1], [3] and Dunn [12]. The ideas were partly motivated by the problems caused by the binary or crisp assignment of data to unique clusters as for instance in the case of the popular c-means clustering algorithm. Handling ambiguous and noisy data in order to overcome these problems was one important issue. Although such concepts of robustness were part of the motivation for introducing fuzzy clustering, serious attempts to a rigorous analysis of robustness issues in fuzzy clustering have not been made until the mid-nineties. © 2009 Springer-Verlag Berlin Heidelberg.