Rough clustering using generalized fuzzy clustering algorithm

In this paper, we present a rough k-means clustering algorithm based on minimizing the dissimilarity, which is defined in terms of the squared Euclidean distances between data points and their closest cluster centers. This approach is referred to as generalized rough fuzzy k-means (GRFKM) algorithm. The proposed method solves the divergence problem of available approaches, where the cluster centers may not be converged to their final positions, and reduces the number of user-defined parameters. The presented method is shown to be converged experimentally. Compared to available rough k-means clustering algorithms, the proposed method provides less computing time. Unlike available approaches, the convergence of the proposed method is independent of the used threshold value. Moreover, it yields better clustering results than RFKM for the handwritten digits data set, landsat satellite data set and synthetic data set, in terms of validity indices. Compared to MRKM and RFKM, GRFKM can reduce the value of Xie–Beni index using the handwritten digits data set, where a lower Xie–Beni index value implies the better clustering quality. The proposed method can be applied to handle real life situations needing reasoning with uncertainty.