模糊支持向量机中隶属度的确定与分析

Determination and Analysis of Fuzzy Membership for SVM

针对目前模糊支持向量机方法中,一般使用特征空间中样本与类中心之间的距离关系构建隶属度函数的不足,提出了一种新的有效地反映样本不确定性的隶属度计算方法———基于样本紧密度的隶属度方法。在确定样本的隶属度时,不仅考虑了样本与类中心之间的关系,还考虑了类中各个样本之间的关系,并采用模糊连接度来度量类中各个样本之间的关系。将其应用于模糊支持向量机方法中,较好地将支持向量与含噪声或野值样本区分开。实验结果表明,采用模糊支持向量机方法,其分类错误率比采用支持向量机方法的错误率低,在使用的3种隶属度函数中,采用基于紧密度隶属度的模糊支持向量机方法抗噪性能最好,分类性能最强。

Relative to the fuzzy membership as a function of distance between the point and its class center in feature space for some current fuzzy support vector machines, a new and more effective fuzzy membership as a function of affinity among samples is proposed for the measurement of the inaccuracy of samples. The fuzzy membership is defined by not only the relation between a sample and its cluster center, but also those among samples, which is described by the fuzzy connectedness among samples. The fuzzy membership based on the affinity among samples for support vector machine effectively distinguishes between support vectors and outliers or noises. Experimental results show that the fuzzy support vector machine, based on the affinity among samples is more robust than the traditional support vector machine, and fuzzy support vector machines taken by other two fuzzy memberships.