Fuzzy clustering with multiple kernels in feature space

While classical kernel-based clustering algorithms are based on a single kernel, in practice it is often desirable to base clustering on combination of multiple kernels. In [1], we considered a fuzzy c-means with multiple kernels in observation space (FCMK-OS) algorithm which constructs the kernel from a number of Gaussian kernels and learns a resolution specific weight for each kernel function in each cluster. The FCMK-OS did not have a closed form expression to update the kernel weights. Moreover, it derives the fuzzy c-means in input space with kernelization of the metric. Thus, it can not handle nonlinear partitioning of the data. In this paper, we propose a fuzzy c-means with multiple kernels in feature space (FCMK-FS) algorithm which extends the fuzzy c-means algorithm with an adaptive multiple kernel learning setting. The incorporation of multiple kernels and unsupervised adjusting of the kernel weights in each cluster makes the choice of the kernels less crucial and allows better characterization and adaptability to each individual cluster. Experiments on both toy and real data sets demonstrate the effectiveness of the proposed FCMK-FS algorithm.