Diversity-induced fuzzy clustering

Abstract

Granular computing plays an important role in human reasoning and problem solving, a reasonable granulation method is important in practical tasks. Clustering is one of the most common methods of granulation, learning clear and correct grouping structure of a data set is a key pursuit for clustering algorithm. An excellent clustering algorithm needs to not only explore similar characteristics of individual group but also to pay attention to ensure higher discrimination among different centers. Ignoring the between-cluster variation will lead to a phenomenon that multiple learned centers concentrate to one point, it happens especially when confronted with datasets exist overlapping regions among clusters. To overcome this issue, we model the diversity information in-between different clusters and measure it with a statistical dependence metric Hilbert Schmidt Independence Criterion (HSIC), and then develop a Diversity-induced Fuzzy C-Means clustering algorithm framework based on traditional Fuzzy C-Means algorithm, which can minimize the within-cluster dispersion and maximize between-clusters separation simultaneously. The formula of updating center attracts the points have the same group with it as well as excludes the impact from other clusters. We analyze the convergence of proposed method under the alternating minimizing optimization fashion, and discuss the sensitivity of parameters in algorithm for clustering performance. The reasonability and advantages of proposed method also have been explained by simulation study. Further, three types of DiFCM methods by using different HSIC form carry out on UCI and image data sets, all experimental results confirm the outstanding of the proposed method.