一种基于决策粗糙集的模糊C均值聚类数的确定方法

Determining Clustering Number of FCM Algorithm Based on DTRS

Fuzzy C-Means(FCM)是模糊聚类中聚类效果较好且应用较为广泛的聚类算法,但是其对初始聚类数的敏感性导致如何选择一个较好的C值变得十分重要。因此,确定FCM的聚类数是使用FCM进行聚类分析时的一个至关重要的步骤。通过扩展决策粗糙集模型进行聚类的有效性分析,并进一步确定FCM的聚类数,从而避免了使用FCM时不好的初始化所带来的影响。文中提出了一种基于扩展粗糙集模型的模糊C均值聚类数的确定方法,并通过图像分割实验来验证聚类的效果。实验通过比对不同聚类数下分类结果的代价获得了一个较好的分割结果,并将结果与Z.Yu等人于2015年提出的蚁群模糊C均值混合算法(AFHA)以及提高的AFHA算法(IAFHA)进行对比,结果表明所提方法的聚类结果较好,图像分割效果较明显,Bezdek分割系数比AFHA和IAFHA算法的更高,且在Xie-Beni系数上也有较大优势。

Fuzzy C-Means （FCM）, as the most popular algorithm of the soft clustering, has been extensively used to make compact and well separated clusters. However, its sensitivity to initial cluster number makes choosing a better C value become very important. So it is an important step to determine the number of FCM clustering when we use FCM to do cluster analysis. In this paper, the extended decision-theoretic rough sets（DTRS） model is applied for the purpose of clustering validity analysis which could overcome the defect of the FCM algorithm. We proposed the method for de- termining clustering number of FCM algorithm based on DTRS, and we verified the effect of the clustering by image segmentation. Good segmentation results can be obtained when we compare the cost of different number of clusters. We compared our results with the ant colony fuzzy c-means hybrid algorithm （AFHA）,which was proposed by Z. Yu et al in 2015, and the improved AFHA （IAFHA）. The experimental results show that our clustering result is better in Bezdek partition coefficient with a higher value than AFHA and IAFHA algorithms, and in the Xie-Beni index as well.