基于快速确定隐层神经元数的BP神经网络算法

根据多项式理论构造一种以正交多项式作为隐层神经元激活函数的PP神经网络模型。针对该网络提出一种算法，即一种隐层的激励函数为正交多项式及其神经元数目可快速确定的算法。首先通过数学证明从理论上验证了该算法的有效性。然后利用计算机对该算法进行仿真与校验，并与传统的PP算法进行比较。结果表明该算法不仅突破了传统PP神经网络的局限性，如收敛速率慢、最佳隐神经元数难确定等，而且能够达到更高的工作精度，从而从实验上验证了该算法的有效性。

Algorithm for BP Neural Networks by Identifying Numbers of Hidden Layer Neurons Quickly

Based on polynomial curve-fitting theory, an orthogonal basis feed-forward neural network is constructed.The model is adopted by a three-layer structure, where the hidden-layer neurons are activated by orthogonal polynomial functions. In view of the network, an algorithm is proposed that a kind of hidden layer activation function is the orthogonal polynomial and the number of neurons can be ctuickly determined. Through mathematical proof , the validity of the algorithm is theoretically proved. The algorithm is verified by computer simulations, comparing with the conventional BP algorithm. The results show that this algorithm not only breaks through the traditional BP neural network limitalions, such as slow convergence rate, optimal number of hidden neurons that difficult to be determined, but also can achievc higher precision. The effectiveness of the designed algorithm is validated.