A robust kernel-based fuzzy local neighborhood clustering with quadratic polynomial-center clusters

Abstract

Aiming at the problem that existing fuzzy clustering with quadratic polynomial prototype cannot effectively deal with the uneven illumination images, a robust kernel-based fuzzy local neighborhood clustering-related algorithm based on quadratic polynomial is proposed. In this paper, the samples and cluster centers of fuzzy clustering with quadratic polynomial prototype are firstly mapped into the high-dimensional feature space. Furthermore, an optimization model of kernel-based fuzzy local neighborhood information clustering with quadratic polynomial prototype is constructed by the induced kernel distance metric. Then the iterative algorithm of membership and coefficient matrix of the quadratic polynomial prototype is proposed by Lagrange multiplier method and numerical algebra. In the end, the convergence of the proposed is strictly proved by using the combination of Zangwill theorem and bordered Hessian matrix. Experimental results show that the proposed algorithm outperforms existing fuzzy clustering with quadratic polynomial prototype, and it can effectively resolve the segmentation problem of inhomogeneous image and has very high accuracy in segmenting MRI brain images with a certain intensity of noise or bias field.