How KLFCM Works—Convergence and Parameter Analysis for KLFCM Clustering Algorithm

Abstract

KLFCM is a clustering algorithm proposed by introducing K-L divergence into FCM, which has been widely used in the field of fuzzy clustering. Although many studies have focused on improving its accuracy and efficiency, little attention has been paid to its convergence properties and parameter selection. Like other fuzzy clustering algorithms, the output of the KLFCM algorithm is also affected by fuzzy parameters. Furthermore, some researchers have noted that the KLFCM algorithm is equivalent to the EM algorithm for Gaussian mixture models when the fuzzifier λ is equal to 2. In practical applications, the KLFCM algorithm may also exhibit self-annealing properties similar to the EM algorithm. To address these issues, this paper uses Jacobian matrix analysis to investigate the KLFCM algorithm’s parameter selection and convergence properties. We first derive a formula for calculating the Jacobian matrix of the KLFCM with respect to the membership function. Then, we demonstrate the self-annealing behavior of this algorithm through theoretical analysis based on the Jacobian matrix. We also provide a reference strategy for determining the appropriate values of fuzzy parameters in the KLFCM algorithm. Finally, we use Jacobian matrix analysis to investigate the relationships between the convergence rate and different parameter values of the KLFCM algorithm. Our experimental results validate our theoretical findings, demonstrating that when selecting appropriate lambda parameter values, the KLFCM clustering algorithm exhibits self-annealing properties that reduce the impact of initial clustering centers on clustering results. Moreover, using our proposed strategy for selecting the fuzzy parameter lambda of the KLFCM algorithm effectively prevents coincident clustering results from being produced by the algorithm.