Fourier三角基神经元网络的权值直接确定法

A Direct-Weight-Determination Method for Trigonometrically-Activated Fourier Neural Networks

根据Fourier变换理论,本文构造出一类基于三角正交基的前向神经网络模型。该模型由输入层、隐层、输出层构成,其输入层和输出层采用线性激励函数,以一组三角正交基为其隐层神经元的激励函数。依据误差回传算法(即BP算法),推导了权值修正的迭代公式。针对BP迭代法收敛速度慢、逼近目标函数精度较低的缺点,进一步提出基于伪逆的权值直接确定法,该方法避免了权值反复迭代的冗长过程。仿真和预测结果表明,该方法比传统的BP迭代法具有更快的计算速度和更高的仿真与测试精度。

Based on the Fourier transformation theory, a feed-forward neural network using trigonometric orthogonal activation-functions is constructed in this paper. The neural network adopts a three-layer structure, where the input and output layers employ linear activation functions, while the hidden-layer neurons are activated by a series of trigonometric orthogonal functions. In this paper, we first derive its weight-updating formula by adopting the standard BP training algorithrn. More importantly, a pseudo-inverse method is proposed as well, which directly determines the weights of the neural network without iterative BP training. Simulation results show that the direct-weight-determination method is more efficient and accurate than the conventional BP iterative-training algorithms.