特征加权的模糊C聚类算法

Feature-weighted fuzzy C clustering algorithm

参照文献[5]中将K-means聚类算法与特征权重优化相结合的方法,推导出FCM聚类算法与特征权重优化相结合的优化迭代公式,形成加权FCM算法。将加权FCM算法中计算聚类均值项的公式代入到计算隶属度的更新公式和特征权重的更新公式中,得到加权FCM扩展算法。由于这个扩展算法消去了均值项,它对于有序属性和无序类别属性的隶属度和特征权重的更新公式具有统一的形式,因此可以很方便地应用到混合属性数据集的加权聚类分析中来。该算法的收敛性分析与FCM类似,算法迭代结束后能给出一组优化的特征权重值。仿真实验结果与WKMeans算法的结果基本一致,说明该方法在优化混合属性数据集的特征权重时是有效的。

Several optimal iterative formulas are deduced by an integration between the FCM clustering algorithm and the optimization of feature weight based on the forward works. Then an extended algorithm of feature-weighted fuzzy C clustering algorithm can be obtain which is deduced from the FCM clustering algorithm and the optimization of feature weight by inserting the formula of computing mean- point of cluster into the updating formula of membership grade and feature weight. This kind of extended algorithm can be applied to clustering analysis of those data sets containing both order attributes and out-of-order attributes. This method is valid by several experi- ments and some compares with WKMeans. At last, it points out that this method can be applied to the reduction of hybrid attributes.