| 实现减小Fuzzy聚类失真的一种方法 |
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| 引用本文： | 苗丽,谷云东,冯艳宾,王加银. 实现减小Fuzzy聚类失真的一种方法[J]. 北京师范大学学报(自然科学版), 2003, 39(5): 601-605 |
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| 作者姓名： | 苗丽 谷云东 冯艳宾 王加银 |
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| 作者单位： | 北京师范大学数学系,100875,北京 |
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| 基金项目： | 国家自然科学基金;60174013; |
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| 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，并借助实例验证了该算法的有效性．
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| 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 |
| 修稿时间： | 2003-01-14 |
A METHOD TO DECREASE THE DISTORTION OF FUZZY CLUSTERING |
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| Miao Li Gu Yundong Feng Yanbin Wang Jiayin. A METHOD TO DECREASE THE DISTORTION OF FUZZY CLUSTERING[J]. Journal of Beijing Normal University(Natural Science), 2003, 39(5): 601-605 |
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| Authors: | Miao Li Gu Yundong Feng Yanbin Wang Jiayin |
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| Abstract: | 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. |
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| Keywords: | fuzzy clustering dividing level of fuzzy clustering perturbation level cut matrices distortion of fuzzy clustering |
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