基函数神经网络和再生核函数关系  

Relationship Between Basis-Function Neural Networks and Reproducing Kernel Function

作　　者：南东[1] 刘力军[2] 

机构地区：[1]北京工业大学应用数理学院,北京100124 [2]大连民族学院应用数学系,大连116600

出　　处：《北京工业大学学报》2014年第9期1428-1431,共4页Journal of Beijing University of Technology

基　　金：国家自然科学基金资助项目(61002039)

摘　　要：主要研究了基函数神经网络和再生核函数之间的关系,证明了当基函数神经网络的激活函数φ(x)∈C[-1,1]n时,基函数神经网络实质就是一个再生核函数,并且给出了基函数神经网络的再生核数学表示形式.同时,把这个结论推广到一般前馈神经网络结构上,得到一般前馈神经网络实质上也有一个再生核函数表示的结果,并给出了相应的数学表示形式.The authors studied the relationship between basis function neural networks and the reproducing kernel function in this paper. With the condition of that activation function φ（x）∈C[ - 1, 1 ]n, it was proved that the basis-function neural networks could be represented by a serious of reproducing kernel functions. Mathematical expressions of reproducing kernel functions were given to the basis-function neural networks. To the general feedforward newral networks, it was also representated by some reproducing kernel functions. Mathematical represeutations of reproducing kernel functions were given to the general feedforword neural networks as a conclusion.

关 键 词：基函数神经网络 再生核函数 前馈神经网络 逼近能力 

分 类 号：O235[理学—运筹学与控制论] TP183[理学—数学]