Viewpoint-Based Kernel Fuzzy Clustering With Weight Information Granules

Yiming Tang, Zhifu Pan, Witold Pedrycz, Fuji Ren, Xiaocheng Song

Abstract: Domain knowledge can be introduced into fuzzy clustering with the aid of information granules, embodied by the concept of viewpoints. For such kind of fuzzy clustering methods, the strategy of acquisition of viewpoints has not been fully developed. Furthermore a way of determining the related information granules deserves more attention. Having these problems in mind, in this study, the density Viewpoint-based Weighted Kernel Fuzzy Clustering (VWKFC) algorithm is proposed. First, the kernel-based hypersphere density initialization (KHDI) algorithm is presented as a certain prerequisite, in which the kernel distance is utilized instead of the Euclidean distance. Besides, a novel density radius is put forward. Second, the concept of the weight information granule is established, which incorporates two parts. The feature weight matrix is provided, where different weights are assigned to different features to reduce the influence of unrelated features. Meanwhile a sample weight is assigned to each data point, thus the influence of noise and outliers on clustering can be reduced to a certain extent. Third, the data point with the highest local density obtained by KHDI is regarded as the density viewpoint. Then we combine kernel mechanism, density viewpoints, weight information granules and a maximum entropy regularization to design the VWKFC algorithm, and prove its convergence. Experimental results validate that VWKFC is superior over eight related clustering algorithms with regard to five evaluation indexes, especially when processing high-dimensional data. It has been shown that VWKFC makes the selection of initialized cluster centers and viewpoints more reasonable, and obtains better clustering results, and achieves higher convergence speed.