摘要
研究Fuzzy聚类的失真问题 .首先 ,基于Fuzzy相似矩阵的传递闭包给出一种相似矩阵的“进化”方法 .随后 ,从理论上证明了由该方法得到的矩阵一定是等价矩阵 .该等价矩阵与传递闭包具有相同的聚类类群 ,并且它与原相似矩阵的距离不大于传递闭包与原相似矩阵的距离 .最后 ,给出一个基于上述相似矩阵“进化”思想的聚类算法 。
A new perturbative method is proposed to solve the distortion problem of clustering based on transitive closure. First, the method of constructing new matrix based on transitive closure is introduced. Then, it is proved that the new matrix must be an equivalent matrix. The new equivalent matrix has the same clustering efficacy with respect to the transitive closure of original similar matrix, but the distance between the new equivalent matrix and original similar matrix is not more than that of the transitive closure of original similar matrix. Finally, an clustering algorithm based on the new euivalent matrix is given and its validity is verified by some examples.
出处
《北京师范大学学报(自然科学版)》
CAS
CSCD
北大核心
2003年第5期601-605,共5页
Journal of Beijing Normal University(Natural Science)
基金
国家自然科学基金资助项目 (6 0 174 0 13)
教育部博士点基金资助项目 (2 0 0 2 0 0 2 70 13)
关键词
Fuzzy聚类
失真
分界水平
摄动
水平截矩阵
模糊相似矩阵
聚类分析
fuzzy clustering
dividing level of fuzzy clustering
perturbation
level cut matrices
distortion of fuzzy clustering