Multiple Prototype Model for Fuzzy Clustering
In partitional fuzzy clustering, each cluster is characterized by two items: its centroid and its membership function, that are usually interconnected through distances between centroids and entities (as in fuzzy c-means).
We propose a different framework for partitional fuzzy clustering which suggests a model of how the data are generated from a cluster structure to be identified. In the model, we assume that the membership of each entity to a cluster expresses a part of the cluster prototype reflected in the entity. Due to many restrictions imposed, the model as is leads to removing of unneeded cluster prototypes and, thus, can serve as an index of the number of clusters present in data.
A comparative experimental study of the method fitting the model, its relaxed version and the fuzzy c-means algorithm has been undertaken. In general, the study suggests that our methods can be considered a model-based parallel to the fuzzy c-means approach. Moreover, our generic version can be viewed as a device for revealing “the natural cluster structure” hidden in data.
KeywordsCluster Structure Fuzzy Cluster Gradient Projection Method Major Iteration Comparative Experimental Study
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