Facilitating the generalized Lorentzian kernel function for fuzzy c-means clustering

Fuzzy c-means (FCM) algorithm is considered as suitable algorithm for data clustering. However, the FCM has considerable trouble in a noisy environment and are inaccurate with large numbers of different sample sized clusters, because of its Euclidean distance measure objective function for finding the relationship between the objects. Those drawbacks can be solved by the Gaussian kernel mapping of the Alternative FCM (AFCM). This paper realized the drawbacks of AFCM and introduced a generalized Lorentzian kernel function for fuzzy c-means clustering. Experiments are performed with artificially generated data and then the proposed methods can be implemented to cluster the Iris database into three clusters for the classes iris setosa, iris versicolour and iris virginica. Experimental results show, the Generalized Lorentzian Fuzzy c-means (GLFCM) can cluster data with outliers and unequal sized clusters. The GLFCM yields better cluster than K-means (KM), FCM, Alternative fuzzy c-means (AFCM), Gustafson-Kessel (GK) and Gath-Geva (GG). It takes less iteration than that of AFCM to converge. Its partition index (SC) is better than the others.