Alpha-Cut Implemented Fuzzy Clustering Algorithms and Switching Regressions
IEEE Transactions on Systems Man and Cybernetics Part B (Cybernetics)
In the fuzzy c-means (FCM) clustering algorithm, almost none of the data points have a membership value of 1. Moreover, noise and outliers may cause difficulties in obtaining appropriate clustering results from the FCM algorithm. The embedding of FCM into switching regressions, called the fuzzy c-regressions (FCRs), still has the same drawbacks as FCM. In this paper, we propose the α-cut implemented fuzzy clustering algorithms, referred to as FCMα, which allow the data points being able to
... being able to completely belong to one cluster. The proposed FCMα algorithms can form a cluster core for each cluster, where data points inside a cluster core will have a membership value of 1 so that it can resolve the drawbacks of FCM. On the other hand, the fuzziness index m plays different roles for FCM and FCMα. We find that the clustering results obtained by FCMα are more robust to noise and outliers than FCM when a larger m is used. Moreover, the cluster cores generated by FCMα are workable for various data shape clusters, so that FCMα is very suitable for embedding into switching regressions. The embedding of FCMα into switching regressions is called FCRα. The proposed FCRα provides better results than FCR for environments with noise or outliers. Numerical examples show the robustness and the superiority of our proposed methods.