LOO (Leave One Out) is commonly used to evaluate the generalization performance of an SVM (Support Vector Machine) , the disadvantage of which is time consuming. In order to decrease the time cost,several LOO bounds are proposed. The most famous bounds are Joachims bound and Jaakkola-Haussler bound. Based on the two boumds, the generalization performance of an SVM can be evaluated properly with decreased time cost. This paper gives the proof of the equivalence of the two bounds in an SVM with RBF (Radial Basis Function) kernel, analyzes the two bounds theoretically, proposes an advanced Joachims bouud,compares the LOO error,Joachims bound, Jaakkola-Haussler bound and the advanced Joachims bound by simulated experiments. Results show that the advanced Joachims bound is closer to the LOO error,and is a better method to evaluate the generalization performance of an SVM.%留一法(Leave One Out,LO0)错误率是评价支持向量机(Support Vector Machine,SVM)性能最准确方法,100错误率越小,SVM泛化性能越好.但LOO实现起来较为费时.因此人们提出了LOO错误率的各种上界作为近似,最有代表性的是Joachims上界和Jaakkola-Haussler上界.基于LO0上界的SVM泛化性能评价方法不但较为准确,而且耗时大大减小.本文首先证明了在径向基函数(Radial Basis Function,RBF)为核函数的SVM中,Joachims上界和JaakkolaHaussler上界是等价的;其次对Joachims上界进行理论分析,指出了其不足之处,并予以改进,得到了改进的Joachims上界;最后通过实验对LOO错误率、Jaakkola-Haussler上界、Joachims上界和改进的Joachims上界进行了比较,结果显示改进的Joachims上界比Jaakkola-Haussler上界和Joachims上界更加接近LOO错误率,是一种更加准确的SVM泛化性能评价方法.
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