基于对应分析的冗余模糊C均值聚类算法研究

针对模糊C均值聚类（FCM）算法聚类原型最适合于球状类型簇的特点，提出了基于类间分离度和类内紧缩度加权的冗余聚类中心的FCM算法，即先将大簇或者延伸形状的簇（非凸）采用加权FCM算法分割成多个小类（冗余类），从而规避FCM算法对初始聚类中心敏感的弱点．由于隶属度划分矩阵的元素是每个样本隶属于各冗余类的隶属度值，因此将其作为各冗余类的类特征，通过对应分析得到冗余类的新特征，再次采用加权FCM算法进行冗余类合并，最后达到分类效果．以代表曲线分割和曲面分割分类问题的3个典型数据集为算例，结果表明该方法能够识别不规则的簇，解决了FCM算法对初始聚类中心敏感的缺陷．

Study of multi-prototype fuzzy C-means clustering algorithm using correspondence analysis

Novel fuzzy C-means(FCM) clustering algorithm based on inter-class separation and intra-class contraction was proposed,for the purpose of solving the problems that the FCM algorithm was sensitive to the initial prototypes,and it did not work well unless the shape of clusters was convex.Large clusters or elongated shaped clusters were first divided into lots of small clusters using weighted FCM.The elements of the fuzzy membership matrix were regarded as the features of small clusters,for they represented the degrees that samples belong to different classes.Correspondence analysis was applied to get the new features of small clusters,and small clusters were merged by using the weighted FCM again to accomplish clustering.Experiment results on three typical datasets which can represent the clustering problems of curve segmentation and surface segmentation show that this method can well recognize irregular clusters,and validly avoid the dependency of the FCM on initial prototypes as well.