Gauss诱导核模糊c均值聚类算法  

GAUSS-INDUCED KERNEL FUZZY C-MEANS CLUSTERING ALGORITHM

作　　者：文传军[1] 詹永照[2] 

机构地区：[1]常州工学院数理与化工学院,江苏常州213002 [2]江苏大学计算机科学与通信工程学院,江苏镇江212013

出　　处：《计算机应用与软件》2017年第8期257-264,295,共9页Computer Applications and Software

基　　金：国家自然科学基金项目(61170126);常州工学院校级课题(YN1305)

摘　　要：针对核模糊聚类算法优异的非线性表达能力,提出一种Gauss诱导核模糊c均值聚类算法(GIKFCMs)。首先,基于核目标函数和梯度法,得到特征空间聚类中心表达式,并通过内积运算得到聚类中心与样本的核矩阵表达式。其次,取核目标函数中的核函数为Gauss核函数,并利用梯度法得到输入空间聚类中心表达式。最后将聚类中心与样本的核矩阵代入输入空间聚类中心表达式中,从而得到GIKFCMs核聚类中心计算方法,同时得到相应的GIKFCMs核聚类算法。研究GIKFCMs算法的相关性质,分析算法的收敛性和初始化约束。GIKFCMs算法克服了原有核聚类算法在收敛性与初始化约束方面的缺陷。通过仿真实验验证了该算法的有效性。Aiming at the excellent nonlinear expression ability of the kernel fuzzy clustering algorithm, this paper proposes a Gauss-induced kernel fuzzy c-means clustering algorithm. Firstly, based on the kernel objective function and the gradient method, the central expression of the feature space clustering is obtained, and the kernel matrix expression of the cluster center and the sample is obtained by the inner product operation. Secondly, the kernel function in the kernel objective function is Gauss kernel function, and the input spatial clustering center expression is obtained by using the gradient method. Finally, the kernel matrix of the clustering center and the sample is substituted into the input space clustering center expression to get the new clustering center calculation method of GIKFCMs, and the corresponding GIKFCMs kernel clustering algorithm is obtained. In this paper, we studied the properties of GIKFCMs and analyzed the convergence and initialization constraints of the algorithm. The algorithm overcomes the shortcomings of the original kernel clustering algorithm in convergence and initialization constraints. The effectiveness of the proposed algorithm is verified by simulation experiments. In addition, this paper also corrects the error of linear kernel FCM and FCM algorithm equiva-lence.

关 键 词：核方法 模糊聚类 非线性映射 核聚类中心 算法等价性证明 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]