广义多变量模糊C均值聚类算法

A general multivariable fuzzy C-means clustering algorithm

模糊聚类算法为了保证算法的收敛性,要求模糊指标m取值大于1,这限制了算法的普适性。提出广义多变量模糊C均值聚类算法(GMFCM),在多变量模糊C均值聚类算法(MFCM)的基础上,利用粒子群优化算法对分量模糊隶属度进行优化估计,进而将模糊指标拓展到m>0的情况,同时采用梯度法得到算法聚类中心迭代公式。GMFCM理论分析了模糊指标m扩展的原理,研究了模糊指标m在不同取值情况下的性质,解释了模糊指标m的实际意义,讨论了GMFCM算法的收敛性。GMFCM继承了MFCM算法的样本分量区分性能,弥补了MFCM算法聚类中心分量与样本分量重合时的不完备性,突破了模糊聚类算法对参数m的约束,提高了模糊聚类算法的普适性。基于gauss数据集和UCI数据集的仿真测试验证了所提算法的有效性。

That the fuzzy index m must be larger than I can guarantee the convergence of the fuzzy clustering algorithm, however, it also restricts the universality of the clustering algorithm. We propose a novel clustering algorithm called the general multivariable fuzzy C-means clustering （GMFCM）. Based on multivariable fuzzy C-means clustering （MFCM）, the particle swarm optimization algorithm （PSO） is used to perform the optimization estimation on the fuzzy memberships of the GMFCM, thus the scope of the fuzzy index m is extended to m〉0, and the iterative formula of clustering center is derived by the gradient method for the GMFCM. We prove the thereom of new m value scope theoretically and discuss the convergence of the GMFCM. The GMFCM removes the restriction of the fuzzy clsutering on m, and makes up the incompleteness of the MFCM algorithm when the clustering center components and the sample components overlap. Simulation experiments prove the effectiveness of the GMFCM.