粒子群高斯诱导核模糊C均值聚类算法

摘要

为了避免陷入梯度法局部极值以提升模糊聚类算法聚类性能,提出 PSO高斯诱导核模糊 C均值聚类算法(PSO Gauss-induced kernel fuzzy C-means clustering algorithm,PSO-GIKFCM).首先将高斯核函数应用于模糊C聚类算法(FCM)目标函数,得到高斯核模糊聚类目标函数.然后在高斯核特征空间和输入空间利用梯度法得到两空间聚类中心,将特征空间聚类中心与样本的内积核矩阵代入输入空间聚类中心,从而得到高斯诱导核的聚类中心.最后在解空间利用粒子群算法(PSO)对模糊隶属度进行寻优估计,并结合目标函数和聚类中心构成PSO-GIKFCM参数估计迭代流程.PSO-GIKFCM算法基于粒子群算法保证其收敛性,聚类中心仅为模糊隶属度的函数,PSO生物进化算法在解空间全局寻找优解,且将模糊指标扩展为大于0的情况.通过仿真实验验证了所提出算法的有效性.%In order to avoid the local extremum of gradient method and improve the clustering performance of fuzzy clustering algorithm, PSO-GIKFCM algorithm(PSO Gauss-induced kernel fuzzy C-means clustering algo-rithm) is proposed. First of all,the Gauss kernel function is applied to the fuzzy C clustering algorithm(FCM) ob-jective function and the Gauss kernel objective function is obtained. Secondly in the Gauss kernel feature space and input space two spatial clustering centers are obtained by using the gradient method,then the inner product kernel matrix is gained between the feature space clustering center and the sample and putted into the input space cluste-ring center,so as to get the clustering center of Gauss induced kernel. Finally, the particle swarm optimization (PSO) is used to optimize the fuzzy membership in the fuzzy membership solution space,and the iterative process of the PSO-GIKFCM parameter estimation is constructed by combining the objective function and the clustering cen-ter. Particle swarm optimization algorithm ensures the convergence of PSO-GIKFCM algorithm and the clustering center is only the function of the fuzzy membership. Simulation results show the effectiveness of the proposed algo-rithm.