摘要
针对核空间中模糊聚类算法的有效性评价问题,以核非线性映射为工具,将Xie-Beni指标推广到核Hilbert空间,得到其对应的核化形式,并指出该核化指标与VLL指标的区别和联系.在此基础上,通过比较实验,研究了核化的Xie-Beni指标对高斯核宽度β和模糊指数m的稳定特性.结果表明,核化的Xie-Beni指标较之VLL等其他指标具有更好的性能和可靠性,可优先作为核模糊聚类算法的有效性判据.
With the help of the nonlinear mapping defined by kernel function implicitly, the noted Xie-Beni index for fuzzy c-means clustering is generalized into the kernel-defined Hilbert space. And the relation between the kernelized version of Xie-Beni and another index VLL is also investigated. Then, the performances and the dependencies of these two indices on Gauss kernel-width β and fuzzy exponent m are examined by some benchmark experiments, compared with two previously formulated indices, partition coefficient and partition entropy. The results show the superior performance and reliability of the kernelized Xie-Beni index in comparison to other indices, and it can take priority of being employed as the validity criterion for the kernel fuzzy clustering algorithm.
出处
《控制与决策》
EI
CSCD
北大核心
2007年第7期829-832,835,共5页
Control and Decision
基金
国家自然科学基金项目(60572143)
国家电子对抗技术预研基金项目(NEWL51435QT220401).
