核模糊C均值算法的聚类有效性研究

On Cluster Validity for Kernelized Fuzzy C-Mean Algorithm

针对核模糊C均值聚类(Kernelized Fuzzy C-Means,KFCM)算法的有效性评价,以核非线性映射为工具,将原空间中的六个著名有效性指标推广到高维特征空间,得到其对应的核化形式,并通过数值比较实验考察这些核化指标的性能及其对高斯核宽度β和模糊指数m的敏感特性。结果表明,在所考察的指标中,著名的Xie-Beni指标VXB及其改进指标VK的核化版本具有最好的性能和可靠性,可优先作为KFCM聚类算法的有效性准则。

For the sake of evaluating the quality of cluster results obtained by the KFCM （kernelized fuzzy c-means） algorithm, six noted validity indices for standard FCM are generalized into high-dimensional feature space for the purpose of acquiring their corresponding kernelized expressions. And then, the performances and the dependencies of these kernelized indices on Gauss kernel width β and fuzzy exponent m are examined via some tests of numerical experiments. The results show that, the kernelized versions of the Xie-Beni index VXB and its emendatory index VK are the most effective and reliable of the indices considered, so can be given the priority as the cluster validity criteria for KFCM algorithm.