NEW CLUSTER VALIDITY FOR FUZZY CLUSTERING

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					          NEW CLUSTER VALIDITY FOR FUZZY CLUSTERING

         Jesús Soto Espinosa, Andrés Bueno Crespo, and Antonio Flores Sintas


                                                Abstract

The methods of fuzzy clustering that at the moment are used for pattern recognition or image processing use
cluster validity to determine the optimal partition. In most of the cases, the validation of the partitions
problem constitutes the process to determine the suitable number of cluster. Nevertheless, we must mention
that these methods give an instructions that must be valued suitably by the person who makes the
classification, because they offer good results ad hoc.

We propose a new approach to get more importance to fuzzy partition obtained and to the time it conjugates
the geometric structure of the samples set. We considered this point more important: if we used an fuzzy
clustering algorithm why not use an index in whose calculation fuzzy partition has more weight. So, we will
use the Bayes Error that introduces Flores-Sintas in its works and the indices Gath and Geva. The result will
be an agreed index with the fuzzy logic theory. The paper shows a comparative of several indices with the
proposed one, and as it determines the best partition for the pattern recognition in images.


Keywords: Fuzzy Clustering, Cluster Validity, FCM, Pattern Recognition, Optimal Fuzzy Partitions.