基于样条插值函数的离散过程神经网络训练

Discrete process neural networks training based on spline function

为解决过程神经元网络不能直接输入离散样本的问题,提出基于样条插值函数的离散过程神经网络训练算法。首先,将离散过程样本按采样点分段,在采样区间内分别构造样本和权值的分段样条函数;然后,计算样本函数和权函数的乘积在采样区间上的积分,并将此积分值提交给网络的隐层过程神经元;最后,在输出层计算网络输出。分别采用一次、二次、三次样条函数,设计了三种不同的算法。实验结果表明:一次样条计算效率高,逼近能力差;三次样条计算效率低,但逼近能力好;二次样条在计算效率和逼近能力两方面都比较理想。因此,二次样条函数是离散过程神经网络的较好选择。

To solve the problem of process neural networks （PNN） can not receive discrete samples,this paper proposed the discrete PNN training algorithm based on piecewise spline interpolation function. Firstly, divided sampling interval into several subintervals by sampling points, and then constructed the piecewise spline functions of samples and weights in the sampling interval. Secondly,computed the integrals of the product functions of samples and weights functions in the sampling interval, and submitted to process neurons in hide layer. Finally,obtained the PNN output in output layer. By using a linear spline, quadratic spline,and cubic spline function,designed three different algorithms respectively. The experimental results show that the linear spline has higher computation efficiency and lower approximation ability, the cubic spline has lower computation efficiency and higher approximation ability, the quadratic spline is ideal both in the computation efficiency and approximation ability. Hence,quadratic spline function is a better choice for discrete process neural networks.