针对BP神经网络存在的过拟合问题, 提出了基于Pearson关联度的神经网络预测模型。将传统的基于误差反向传播的BP神经网络中的误差函数替换为Pearson关联度函数, 利用梯度上升法对训练过程中神经网络的连接权重和阈值的调整量进行了推导, 并为调整量添加了动量项用于提高神经网络收敛速度, 然后建立了关联度反向传播预测模型, 并对其权重进行了阈值限制以及增加学习率来防止过拟合。对通用数据集进行时间序列预测实验, 通过与改进的RBF和BP神经网络对比, 表明对于多因素时间序列的预测Pearson关联度BP神经网络的预测误差精度RMSE降低了402, 收敛次数减少1 690代。实现了将关联分析与BP神经网络的结合, 能够在保证效率的同时, 解决过拟合问题, 提高预测精度。

In order to realize the over fitting problem existing in Back Propagation (BP) neural networks, a neural prediction model based on Pearson correlation was designed. It replaces the error function in a BP neural network based on error back propagation with the Pearson correlation function. By means of gradient ascent, the adjustment of connection weights and biases in training process is derived. Meanwhile, momentum is added to this adjustment to improve the convergence speed of the network. The Pearson correlation BP prediction model is built with weight threshold limiting and an increasing learning rate to prevent overfitting. Time series prediction experiments on a standard dataset were performed. The results demonstrate that compared with improved the radial basis function and BP neural networks, the Pearson correlation BP neural network reduces root-mean-square error, and time to convergence in multi-factor time series prediction. Therefore, the Pearson correlation BP neural network realizes the integration of correlation analysis with neural networks, is able to ensure efficiency, and can solve fitting problems in the same time as other methods with higher accuracy.