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分析BP网络过拟合出现时网络学习能力及泛化能力与其他影响因素之间的内在联系,引入复相关系数描述样本复杂性程度;遵循计算不确定性原理和神经网络结构设计的最简原则,类比信息传递过程中的一般测不准关系式,建立了BP网络过拟合出现时,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不确定关系式;通过模拟多种不同类型函数的BP网络过拟合数值模拟实验,确定了关系式中过拟合参数q的取值范围一般为7×10~(-3)～7×10~(-2);依据不确定关系式,导出了在用复相关系数描述样本复杂性和满足给定逼近误差要求下,网络具有较佳泛化能力的隐节点数的计算公式,并验证了其合理性;指出BP网络应用于给定样本集的训练过程中,为改进泛化能力的训练最佳停止方法。
This paper analyzes the inherent relationship between network learning ability and generalization ability and other influencing factors when BP network overfit appears, introduces complex correlation coefficient to describe sample complexity degree, and follows the principle of computational uncertainty and the simplest principle of neural network structure design , The general uncertainty relationship in the process of analogical information transmission, and establishes the training relative error of the training sample set that reflects the network learning ability when the BP network overfitting occurs. Compared with the network performance test that tests the sample set The uncertainty between the error satisfies the formula; by simulating a variety of different types of BP network over-fitting numerical simulation experiments to determine the relationship between the over-fitting parameters q range is generally 7 × 10 ~ (-3 ) ~ 7 × 10 ~ (-2). Based on the uncertainty relation, the calculation of hidden nodes with better generalization ability is derived under the condition that the complex correlation coefficient is used to describe the sample complexity and satisfy the given approximation error Formula and verify its rationality. It is pointed out that BP network can be used to train the best generalization ability in the training process of a given sample set.