分数阶非因果BP神经网络模型

doi:10.3778/j.issn.1002-8331.2012-0072

摘要/Abstract

摘要：

由一阶因果、反因果微分的定义推导出Caputo分数阶因果、反因果微积分，并在此基础上定义Caputo分数阶非因果微积分。将它们分别应用于BP神经网络的反向传播过程中对权值进行处理，产生了Caputo分数阶因果、反因果和非因果BP神经网络模型。为了方便对比，将这些模型分别对波士顿房屋数据集和MNIST数据集进行处理。模拟结果表明：在整数阶因果、反因果和非因果的模型之间，整数阶非因果模型的结果最好；分数阶因果、反因果和非因果模型分别与其相应的整数阶模型进行比较，得出分数阶模型得到的准确率比整数阶的高；在分数阶因果、反因果和非因果的模型之间，非因果的准确性最高。总的来说，Caputo分数阶因果、反因果和非因果微积分都对传统BP神经网络有优化作用，尤其是分数阶非因果微积分的优化效果最好。

关键词: 因果, 反因果, 非因果, Caputo分数阶微积分, BP神经网络

Abstract:

Based on the definition of the first-order causal and the first-order anti-causal derivative, the anti-causal Caputo derivative is deduced. Then a non-causal Caputo derivative can be given. By applying them to the back propagation process of BP neural network to deal with the weight, the causal, anti-causal and non-causal BP neural network model are generated. For the convenience of comparison, these models are processed for the Boston Housing dataset and the MNIST dataset separately. The results of the simulation show that the integer-order, non-causal model has the best results among the integer-order models; Fractional-order causal, anti-causal and non-causal models are compared with their corresponding integer-order models separately, then the results of the fractional- order models are better. The accuracy of the non-causal is the highest among the fractional-order models. In general, Caputo causal, anti-causal and non-causal calculus all have positive influence on BP neural network, especially the fractional-order non-causal calculus has the best effect.

Key words: causal, anti-causal, non-causal, Caputo derivative, BP neural network

黄晶晶，王建宏. 分数阶非因果BP神经网络模型[J]. 计算机工程与应用, 2021, 57(23): 91-97.

HUANG Jingjing, WANG Jianhong. Fractional-Order Non-causal BP Neural Networks Model[J]. Computer Engineering and Applications, 2021, 57(23): 91-97.

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