SMKFC-ER: Semi-supervised multiple kernel fuzzy clustering based on entropy and relative entropy

Abstract

The present study aimed to present a new algorithm called Semi-supervised Multiple Kernel Fuzzy Clustering based on Entropy and Relative entropy (SMKFC-ER) by focusing on external knowledge related to the labeled data. In the proposed method, entropy coefficient and relative entropy divergence measure are applied instead of fuzzifier for unsupervised section and the geometric distance measure for semi-supervised section respectively, by emphasizing on combining unsupervised and semi-supervised sections explicitly. The use of relative entropy and entropy in the objective function results in sharing more consistent concepts for the semi-supervised section, controlling the fuzziness of the extracted clusters, and determining the kernel weights regularly for the unsupervised section. Finally, using relative entropy with entropy simultaneously derives a closed-form solution. The performance and supremacy of the proposed method on non-spherical synthetic and real-world datasets are shown by comparing unsupervised and semi-supervised fuzzy clustering methods.