提出了一种基于正交神经网络的曲线重建方法.该正交神经网络结构与三层前向网络相同,不同的是正交网的隐单元处理函数采用Tchebycheff正交函数,而不是sigmoidial函数.新的曲线重建方法具有利用较少的数据点列将光滑的曲线以较高的精度重建的特点.网络训练采用Givens正交学习算法,由于它不是一种迭代算法,故学习速度快,而且没有网络初始参数的选取问题,网络训练又能避免陷入局部极小解等问题.实验表明,用正交神经网络方法重建的曲线在样本点和非样本点处均具有很高的逼近精度.

This paper presents a new curve reconstruction method based on orthogonal neural network. The orthogonal neural network' s structure is the same as that of the three layered feedforward neural network. The difference is that the processing function of hidden unit of the orthogonal neural network is Tchebycheff orthogonal function instead of sigmoidial function and the calculation of Tchebycheff function is simpler than that of sigmoidial function. The new method uses less samples and reconstructs higher precision smooth curves than previous methods. By adopting a non-iterative Givens learning algorithm, the new network learning algorithm learns fast and can avoid false local minima and the initialization of weights and other parameters. Experiments show that the reconstructed curve using the orthogonal neural network method has high precision not only at learning sample points but also at the non-learning sample points.