Multiple Kernel Relative Entropy Fuzzy C-means Clustering Algorithm

The relative entropy fuzzy c-means (REFCM) clustering algorithm is a classical soft clustering approach. REFCM incorporates relative entropy as a regularization term within the objective function of the fuzzy c-means (FCM) clustering algorithm, effectively enhancing its robustness to noise. However, its effectiveness is mainly limited to the clustering of spherical shapes. The kernel trick technique is applied to the REFCM clustering algorithm, wherein the data is mapped to a suitable feature space using a nonlinear mapping to solve the problem. Combining or selecting kernels is very important for efficient kernel clustering. Therefore, we propose a multiple kernel relative entropy fuzzy c-means clustering algorithm (MKREFCM). This algorithm extends single-kernel learning to multi-kernel learning. By integrating several kernels and automatically adjusting weights, the algorithm's sensitivity to kernel selection in the clustering process is minimized. Finally, experiments on non-spherical datasets demonstrate the effectiveness of the proposed algorithm.