V正交基网络

V Orthonormal Basis Neural Network

为了改进BP网络的收敛速度与连续正交基网络无法逼近非连续函数的问题,构造了一类基于V正交基的前馈神经网络(简称V正交基网络),并研究其收敛性条件与伪逆规则。由于V系统是L2([0,1])上的一类完备的正交函数系,且Fourier-V级数有较快的收敛速度,因此,V正交基网络有较快的收敛速度,且能有效地逼近一类强间断的一元函数。最后,通过仿真实验证明,V正交基网络的收敛速度明显优于传统的BP网络、小波网络与Legendre网络,特别是逼近一类间断点在二进制有理数处的函数时,其优势更加明显。

In order to solve the problem that the convergence rate of BP network is not fast,and the neural networks with continuous orthogonal basis cannot approximate discontinuous functions,this paper constructed a class of feed-forward neural networks with V orthonormal basis（referred to as V orthogonal network）,and investigated its convergence condition and pseudo-inverse rule.For V system is a class of complete orthonormal systems in L2（）,and the convergence rate of Fourier-V series is comparatively fast,the convergence rate of V orthogonal network is also fast,and it can effectively approximate a class of discontinuous functions of one variable.The simulation results also show that the convergence rate of V orthogonal network is obviously faster than that of BP network,wavelet network and Legendre network;if using V orthogonal network to approximate the functions whose breakpoints only appear at dyadic rational,its performance of function approximation becomes much better.