Extension of fuzzy Gustafson-Kessel algorithm based on adaptive cluster merging

The performance of objective function-based fuzzy clustering algorithms depends on the shape and the volume of the clusters, the initialization of the clustering algorithm, the distribution of the data objects, and the number of clusters contained in the data. We propose an extension of Gustafson- Kessel (FGK) fuzzy algorithm by developing adaptive validation criteria for merging of clusters during the unsupervised learning. There are no mathematical methods for solving this optimization task analytically. The performance of the proposed approach was examined on generated and benchmark data sets, and compared to those received by respective fuzzy counterparts. Additionally, its efficiency was tested on data collected from some current real world applications.