最优正则化参数的核FCM聚类算法

Kernel FCM Clustering Algorithm Based on Optimal Regularization Parameters

模糊C均值聚类算法(Fuzzy C-mean,FCM)因随机选取初始聚类中心,造成算法求解过程不稳定(即存在不适定性问题).针对此问题,提出一种最优正则化参数的核FCM算法,首先在核FCM的目标函数中引入正则化项和正则化参数;然后推导出用L曲线法寻优正则化参数所需的迭代更新公式;最后用迭代更新公式设计最优正则化参数的核FCM算法.在UCI测试数据集上的实验结果表明:本文所提算法的平均稳定性较传统FCM提高了5倍,平均准确率和平均召回率也分别提高了30%和33%.本文用L曲线法寻优核FCM的正则化参数是可行的,能有效地抑制FCM的不适定性.

Fuzzy C-mean clustering algorithm（ Fuzzy C-mean,FCM） randomly selected the initial clustering center,Resulting in algorithmic solution to the process of instability（ that is,there are ill-posed problem）. In order to solve this problem,a kernel FCM algorithm with optimal regularization parameters is proposed. First,the regularization term and the regularization parameter are introduced in the objective function of the kernel FCM. Then,the iterative updating formula is needed to optimize the regularization parameters by the curve method. Finally,the kernel FCM algorithm for optimal regularization parameters is designed by using iterative updating formula.The experimental results on the UCI test data set show that the average stability of the proposed algorithm is 5 times higher than that of the traditional FCM,and the average accuracy and average recall rate are increased by 30% and 33% respectively. In this paper,it is feasible to use the L-curve method to find the regularization parameters of the FCM,which can effectively suppress the FCM＇s ill-positivity.