Multiple Kernel Fuzzy Clustering

Abstract

While fuzzy c-means is a popular soft-clustering method, its effectiveness is largely limited to spherical clusters. By applying kernel tricks, the kernel fuzzy c-means algorithm attempts to address this problem by mapping data with nonlinear relationships to appropriate feature spaces. Kernel combination, or selection, is crucial for effective kernel clustering. Unfortunately, for most applications, it is uneasy to find the right combination. We propose a multiple kernel fuzzy c-means (MKFC) algorithm that extends the fuzzy c-means algorithm with a multiple kernel-learning setting. By incorporating multiple kernels and automatically adjusting the kernel weights, MKFC is more immune to ineffective kernels and irrelevant features. This makes the choice of kernels less crucial. In addition, we show multiple kernel k-means to be a special case of MKFC. Experiments on both synthetic and real-world data demonstrate the effectiveness of the proposed MKFC algorithm.