A Hyperbolic Fuzzt k-Means Clustering and Algorithm for Neural Networks
A new fuzzy k-means clustering algorithm is proposed by introducing crisp regions of clusters. Boundaries of the regions are determined by hyperbolas and membership values are given by one or zero in each region. The area between crisp regions is a fuzzy region, where membership values are proportional to distances to crisp regions. Though the traditional hard k-means is a limit of the usual fuzzy k-means, results of the latter are fuzzy and then are not the same as results of the former. On the other hand a new method can produce the same results as those by the hard k-means. An algorithm for neural networks is given and a numerical example is illustrated.
KeywordsVoronoi Diagram Fuzzy Cluster Classification Function Fuzzy Method Learning Neural Network
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