| 摘要: |
| 在商空间理论基础上,提出了基于Fuzzy相似关系和归一化距离的聚类分析方法,用以解决复杂系统的数据结构分析问题.得到了如下结论:(1) 通过引入基于Fuzzy相似关系和归一化距离的分层递阶结构,建立了严格的聚类分析理论描述;(2) 给出了有效的分层递阶结构聚类的快速算法;(3) 给出了两个Fuzzy相似关系或由两个归一化距离诱导的Fuzzy相似关系是同构的充分条件.其中所研究的理论和方法适应于建立在相似关系之上的任何复杂系统的数据结构分析. |
| 关键词: Fuzzy商空间 分层递阶结构 聚类分析 Fuzzy相似关系 归一化距离 同构 |
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| 基金项目:Supported by the National Natural Science Foundation of China under Grant No.60475017 (国家自然科学基金); the National Basic Research Program of China under Grant No.2004CB318108 (国家重点基础研究发展计划(973)); the National Research Foundation for the Doctoral Program of Higher Education of China under Grant No.200403057002 (国家教育部博士点基金) |
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| Cluster Analysis Based on Fuzzy Quotient Space |
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TANG Xu-Qing,ZHU Ping,CHENG Jia-Xing
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| Abstract: |
| In this paper, on the basis of fuzzy quotient space theory, cluster analysis methods based on fuzzy similarity relations and normalized distance are proposed to solve data structure analysis of complex systems. Three conclusions are given: (1) the strictly clustering analysis theoretical description by introducing hierarchical structures of fuzzy similarity relation and normalized distance; (2) the effective and rapid clustering algorithms of their hierarchical structures; (3) a sufficient condition for isomorphic hierarchical structures. These conclusions are suitable to data structure analysis of all complex systems based on similarity relation. |
| Key words: fuzzy quotient space hierarchical structure cluster analysis fuzzy similarity relation normalized distance isomorphism |
