零误差密度最大算法的分析研究

The Analysis of Zero-error Density Maximization Algorithm

前馈神经网络的学习通常以均方误差为目标函数(MSE),易陷入局部极小,而零误差密度最大算法(Z-EDM)以误差在零点的概率密度函数为神经网络新的目标函数,能够达到全局最优.将Z-EDM算法应用到BP网络中,并通过仿真将两者进行了比较,实验结果表明,Z-EDM算法在分类方面要明显优于MSE算法.并且对这一算法进行了分析,可知以优化此目标函数的神经网络的学习仍是基于经验风险最小化原则,通过仿真将基于Z-EDM算法的BP网络与支持向量机(SVM)在两分类方面进行比较,结果表明此算法对于某些数据集具有与SVM近似的性能,但总体上性能仍不及基于结构风险最小化的SVM.

Feed-forward neural networks,which usually takes Mean Square Error criteria（MSE）as cost function,is easily to drop in local minimization.Zero-Error Density Maximization algorithm,s（Z-EDM）using error density at origin as the new cost function can reach global optimization.In this paper,Z-EDM algorithm is applied into BP neural networks and the simulation results show that Z-EDM is clearly more powerful in classifying than MSE.The analysis of Z-EDM algorithm suggests training neural networks with this new cost function is still based on empirical risk minimization principle.Support Vector Machine（SVM）and BP based on Z-EDM are compared in classification.Simulation results show that Z-EDM owns similar performance as SVM in certain datasets,but is generally inferior to SVMwith structural risk minimization principle.