Method of the Kernel-based Maximum Entropy Fuzzy C-means Clustering

Most studies incorporating entropy into the fuzzy c-means clustering (FCM) often overlook the fuzzy coefficient, while considering this coefficient typically involves complex iterative derivation and computation. In this paper, a method of the kernel-based maximum entropy fuzzy c-means clustering (K-MEFCM) is proposed. By preserving the fuzzy coefficient, information entropy is added as a regularization term to the objective function, leading to more balanced results. Moreover, to enhance the algorithm’s stability in noisy environments and its ability to handle non-linear and complex data, the Euclidean distance is replaced with a distance induced by the Gaussian kernel function. The derivation process innovatively utilizes the Lambert function to obtain explicit solutions and derive concise iterative formulas, avoiding the complexity of approximate solutions. Additionally, the k-means++ initialization method is adopted to reduce the influence of randomization. Experimental results validate the excellent performance of the proposed method.

I. Introduction

Cluster analysis, a crucial technology in the realm of data mining, serves as a prominent research area in data analysis and artificial intelligence. Presently, this approach finds extensive applications in image processing, natural language processing, social network analysis, and biology. As we enter the era of big data, the multitude, velocity, and quality of data present substantial challenges for humanity. Enhancing algorithm efficiency by efficiently clustering data has thus emerged as the central focal point within this domain.