We explore an approach to possibilistic fuzzy c-means clustering that avoids a severe drawback of the conventional approach, namely that the objective function is truly minimized only if all cluster centers are identical. Our approach is based on the idea that this undesired property can be avoided if we introduce a mutual repulsion of the clusters, so that they are forced away from each other. In our experiments we found that in this way we can combine the partitioning property of the probabilistic fuzzy c-means algorithm with the advantages of a possibilistic approach . the interpretation of the membership degrees. | Fuzzy Cluster Analysis with Cluster Repulsion Heiko Timm, Christian Borgelt, Christian D¨oring,and Rudolf Kruse Dept. of Knowledge Processing and Language Engineering Otto-von-Guericke-University of Magdeburg Universit¨atsplatz2, D-39106 Magdeburg, Germany timm,borgelt,doering,kruse @ { } Abstract We explore an approach to possibilistic fuzzy c-means clustering that avoids a severe drawback of the conventional approach, namely that the objective function is truly minimized only if all cluster centers are identical. Our approach is based on the idea that this undesired property can be avoided if we introduce a mutual repulsion of the clusters, so that they are forced away from each other. In our experiments we found that in this way we can combine the partitioning property of the probabilistic fuzzy c-means algorithm with the advantages of a possibilistic approach . the interpretation of the membership degrees. 1 Introduction Cluster analysis is a technique for classifying data, ., to divide a given dataset into a set of classes or clusters. The goal is to divide the dataset in such a way that two cases from the same cluster are as similar as possible and two cases from different clusters are as dissimilar as possible. Thus one tries to model the human ability to group similar objects or cases into classes and categories. In classical cluster analysis each datum must be assigned to exactly one cluster. Fuzzy cluster analysis relaxes this requirement by allowing gradual memberships, thus offering the opportunity to deal with data that belong to more than one cluster at the same time. Most fuzzy clustering algorithms are objective function based: They determine an optimal classification by minimizing an objective function. In objective function based clustering usually each cluster is represented by a cluster prototype. This prototype consists of a cluster center (whose name already indicates its meaning) and maybe some additional .
