MISO多元广义多项式神经网络及其权值直接求解

MISO Multivariate Generalized Polynomials Neural Network and its Weights-Direct-Determination

基于多元函数逼近理论,构建一种M ISO(Mu ltip le-Input,S ingle-Output)多元广义多项式神经网络。依据最小二乘原理,推导出基于伪逆的最优权值一步计算公式———简称为权值直接确定法;在此基础上,提出基于指数增长和折半删减搜索策略的隐神经元数自适应增删搜索算法。该新型神经网络具有结构简单的优点,其权值直接确定法、隐神经元增删算法可以避免冗长的迭代计算、局部极小点和学习率难选取等问题,同时解决了传统BP神经网络难以确定隐神经元数这一难题。仿真实验显示其具有训练速度快、逼近精度高和良好的去噪特性等特点。

A new type of MISO （Multiple-Input, Single-Output） multivariate generalized polynomials neural network is constructed based on multivariate function approximation theory. According to least square theorem, a pseudoinverse-based weights-direct-determination method is further presented to deter- mine the neural-weights just in one step. Moreover, on the basis of this weights-direct-determination, a hidden-layer evolution algorithm is proposed based on exponential-groWth and binary-delete-search strate- gy. Theoretical analysis demonstrates that, since the weights-direct-determination method and the hidden- layer evolution algorithm could obtain the optimal weights directly without lengthy iterative BP-training, the constructed neural network could remedy the weakness of conventional BP neural networks, such as the existence of local-minima, choosing of learning-rate as well as the determination of the hidden-layer neurons. Computer simulation results substantiate the advantages of weights-direct-determination method and hidden-layer evolution algorithm for the constructed neural network, in the sense of training speed and high approximation precision.