Research On Fuzzy Clustering Methods Based On Fuzzy C-Means

Clustering is one of the most important methods in unsupervised learning.Clustering methods have been widely applied and studied in recent years.Among different types of clustering methods,fuzzy clustering methods stand out because they can extract the uncertainty and inaccuracy of datum more effectively and accurately.Hence,fuzzy clustering methods have become a research hotspot.For FCM and other fuzzy clustering methods,the introduction of membership degree allows the observations to exert pulling force on centroids of all the clusters,no matter how far the observations are away from these clusters.Besides,as the distance increases,the force increases indefinitely,making the situation worse.In this case,the cluster centroids are inappropriately shifted by FCM,leading to insufficient ability of extracting the essential structure of clusters.To solve these problems,the following ideas are taken into consideration for improving fuzzy clustering methods.(1)To enhance the compactness of clusters by increasing the effect of the observations in the central region of clusters on the cluster centroids which the observations belong to.At the same time,the impact of noise is reduced indirectly,and the robustness of clustering methods is improved.(2)To improve the separability between clusters by highlighting the effect of marginal points on cluster centroids which they don't belong to.The fuzzy boundary regions between clusters are expanded and the robustness of clustering methods is enhanced.Several works are developed in this papers:(1)Gaussian collaborative fuzzy c-means clustering method(GCFCM)is proposed based on standard FCM and GMM by utilizing collaborative clustering technology.The relevant mathematical proof is also provided to demonstrate the characteristics of GCFCM.(2)Adaptive elastic distance is proposed and applied to FCM,and the elastic fuzzy c-means clustering method(EFCM)is proposed.Besides,the spatial neighborhood information is introduced to the elastic fuzzy c-means clustering algorithm,and the adaptive robust fuzzy c-means clustering method(ARFCM)is proposed for image segmentation.(3)L1 norm regularization technology and adaptive relaxation technology are used to solve the noise problem in fuzzy clustering methods.And the robust fuzzy c-means clustering method based on adaptive relaxation is proposed.Through in-deep analysis of the performance of different proposed methods among targeted experiments and UCI benchmark repository,it turns out that the proposed fiuzzy clustering methods can not only solve targeted problems(such as noise,outlier and imbalanced data set),but also show excellent effectiveness when dealing with real-world data sets.It demonstrates strong robustness and excellent comprehensive abilities of the proposed fuzzy clustering methods.