迭代吉洪诺夫正则化的FCM聚类算法

摘要

模糊C均值聚类算法(fuzzy C-means,FCM)存在不适定性问题,数据噪声会引起聚类失真.为此,提出一种迭代Tikhonov正则化模糊C均值聚类算法,对FCM的目标函数引入正则化罚项,推导最优正则化参数的迭代公式,用L曲线法在迭代过程中实现正则化参数的寻优,提高FCM的抗噪声能力,克服不适定问题.在UCI数据集和人工数据集上的实验结果表明,所提算法的聚类精度较传统FCM高,迭代次数少10倍以上,抗噪声能力更强,用迭代Tikhonov正则化克服传统FCM的不适定问题是可行的.%FCM algorithm has the ill posed problem.Regularization method can improve the distortion of the model solution caused by the fluctuation of the data.And it can improve the precision and robustness of FCM through solving the error estimate of solution caused by ill posed problem.Iterative Tikhonov regularization function was introduced into the proposed problem (ITR-FCM),and L-curve method was used to select the optimal regularization parameter iteratively,and the convergence rate of the algorithm was further improved using the dynamic Tikhonov method.Five UCI datasets and five artificial datasets were chosen for the test.Results of tests show that iterative Tikhonov is an effective solution to the ill posed problem,and ITR-FCM has better convergence speed,accuracy and robustness.