BP网络学习能力与泛化能力之间的定量关系式

分析BP网络过拟合时网络学习能力与泛化能力之间的内在联系,引入描述问题复杂性程度的复相关系数,建立了BP网络过拟合时,反映网络学习能力的训练样本集的训练相对误差与表征泛化能力的网络对检验样本集的测试相对误差之间满足的定量关系式.通过模拟若干不同类型函数的BP网络数值建模试验,确定了关系式中过拟合参数q的取值范围为0.007~0.07,指出BP网络应用于给定样本集的训练过程中,具有较佳泛化能力的停止训练方法.

Quantitative Relation Between Learning Ability and Generalization Ability of BP Neural Network

Based on the analysis of the internal relation between learning ability and generalization ability of the overfitting of BP neural network,by the introduction of mulit-correlative coefficient to manifest the complexity of the function,a quantitative uncertainty relation between the fitting relative error of training sample sets and the testing relative error of verifying sample sets,which describe the learning ability and the generalization ability of BP network,respectively,was revealed in the overfitting of BP neural network.Tests of numerical simulation for multi-kinds of different functions were carried out to determine the value distribution (0.007~0.07)of overfitting parameter q in the relation.Based on the quantitative relation,the training method for the improvement of generalization ability in the training process of sample sets using BP neural network was given.