摘要： 基于粗糙集理论，分析等价关系与粒度之间的关系，提出一种基于粒度的粗糙聚类方法。该方法根据数据对象之间的相对相似性形成初始等价关系和等价类，每个等价类对应一个粒度。引入等价关系隶属度因子 ，用于度量等价关系间隶属关系，作为聚类过程一个有效参数，控制聚类的规模。通过迭代计算聚类的有效性，得到优化的聚类结果。聚类过程表明，聚类分析在一个统一的粒度下进行，在样本点之间定义一种等价关系。实验结果证实了该方法的有效性，用规则集描述的聚类结果具有可解释性和合理性。

关键词: 等价关系, 粒度, 粗糙集, 聚类分析

Abstract: This paper analyzes the connection between equivalence relation and granulation based on rough theory. A method of rough clustering based on granulation is presented. The method evaluates relative similarity relation to each object to form initial equivalence relation, and the equivalence class is developed. Each equivalence class may be viewed as a granule consisting of indistinguishable and similarity elements. Using a newly introduced measure, equivalence relation membership, the method evaluates subordination degree of equivalence relation to modify the scale of clustering during clustering process. The optimal clustering result can be obtained by evaluating the cluster validity with various values of similarity thresholds. From the view of granularity, the clustering is a computation under the same granularity. Experimental results show that the method is effective, the clustering results described by rules set are interpretable and rational.

Key words: equivalence relation, granulation, rough set, clustering analysis

中图分类号: 

• TP18