基于商空间的模糊等价关系在聚类分析中的应用  

The application of fuzzy equivalence relation based on the quotient space in cluster analysis

作　　者：张媛[1,2] 沈庆伟[1] 张铃[2] 

机构地区：[1]安徽建筑工业学院电子与信息工程学院,安徽合肥230601 [2]安徽大学计算机科学与技术学院,安徽合肥230601

出　　处：《安徽建筑工业学院学报（自然科学版）》2013年第2期83-86,共4页Journal of Anhui Institute of Architecture(Natural Science)

基　　金：安徽省教育厅自然科学项目(KJ2010B034);安徽省教育厅自然科学项目(KJ2011A059)

摘　　要：提出了一种基于商空间的模糊聚类分析模型,首先采用模糊商空间中粗细粒度的转变及分层递阶的思想对多维属性样本进行降维,其次将所得模型中模糊相容关系矩阵转换为模糊等价关系矩阵,最后根据模糊等价矩阵得出聚类族谱图,从而选取出不同阈值进行聚类分析,有效地解决了多维属性样本的聚类分析问题。A fuzzy clustering analysis model based on the quotient space is proposed. Firstly, the conversion from coarse to fine granularity and the hierarchical structure are used to reduce the multidi- mensional samples. Secondly, the fuzzy compatibility relation matrix of the model is converted into fuzzy equivalence relation matrix. Finally, the diagram of clustering genealogy is generated according to the fuzzy equivalence relation matrix, which enables the dynamic selection of different thresholds to effectively solve the problem of cluster analysis of the samples with multi--dimensional attributes.

关 键 词：商空间 分层递阶 模糊相容关系 模糊等价矩阵 聚类分析 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]