A Fuzzy Genetic Clustering Technique Using a New Symmetry Based Distance for Automatic Evolution of Clusters

Abstract

In this paper a fuzzy point symmetry based genetic clus-tering technique (Fuzzy-VGAPS) is proposed which can de-termine the number of clusters present in a data set as well as a good fuzzy partitioning of the data. A new fuzzy clus-ter validity index, FSym-index, which is based on the newly developed point symmetry based distance is also proposed here. FSym-index provides a measure of goodness of clus-tering on different fuzzy partitions of a data set. Maximum value of FSym-index corresponds to the proper clustering present in a data set. The flexibility of Fuzzy-VGAPS is uti-lized in conjunction with the fuzzy FSym-index to determine the number of clusters present in a data set as well as a good fuzzy partition of the data. The results of the fuzzy VGAPS are compared with those obtained by fuzzy ver-sion of variable string length genetic clustering technique (Fuzzy-VGA) optimizing XB-index. The effectiveness of the Fuzzy-VGAPS is demonstrated on four artificial data sets and two real-life data sets