人工神经网络中的BP算法

BP算法是基本的训练神经网络的方法，通过误差的反向传播，逐层修正连接权值，从而达到训练的目的。我这里做的是用BP的思想来拟合Sin函数（不限于Sin函数）。拟合的结果如下图所示：

工程包的下载链接：http://download.csdn.net/source/2474797

这里贴出NeuralKernel.h和NeuralKernel.cpp的代码。定义了一个单隐层的神经网络，可以设置训练集。

NeuralKernel.h如下：

#ifdef NEURAL_H#else#define NEURAL_H#include <iostream>#include <vector>#include <cmath>#include <stdlib.h>#include <ctime>#include <direct.h>#include <windows.h>using namespace std;#define MAX 128 //隐层的节点个数//本神经网络为单输入 单输出 单隐层的结构class NeuralKernel{public:NeuralKernel();~NeuralKernel();void SetTeacher(vector<double> XX,vector<double> YY);//设置“教师”数据vector<double> GetCurrentOut(double &e); //获取样本集当前输出bool Train();//训练网络void Save();//保存权值到磁盘文件private:vector<double> X;//样本集的Xvector<double> Y;//样本集的Yvector<double> O;//当前输出vector<double> M;//隐层输出double E;//当前总误差int N;//当前训练集规模double aw[MAX],bw[MAX];//两层的权值double inc;//步进长度protected:double GetValue(double x);double Fun(double x);bool Train(double x,double y);};#endif

NeuralKernel.cpp如下：

#include "NeuralKernel.h"NeuralKernel::NeuralKernel(){}NeuralKernel::~NeuralKernel(){}//设置训练集:<XX,YY>void NeuralKernel::SetTeacher(std::vector<double> XX, std::vector<double> YY){X=XX;Y=YY;O.resize(X.size());M.resize(MAX);N=(int)(X.size());srand((unsigned)time(NULL));for(int i=0;i<MAX;i++){aw[i]=((double)(rand()%100)-50.0)/100.0;bw[i]=((double)(rand()%100)-50.0)/100.0;}inc=0.250;}//获取当前输出O 和 总误差 evector<double> NeuralKernel::GetCurrentOut(double &e){unsigned int i;E=0.0;for(i=0;i<N;i++){O[i]=GetValue(X[i]);E+=((O[i]-Y[i])*(O[i]-Y[i]));}E/=2.0;e=E;return O;}//根据整个训练集训练网络bool NeuralKernel::Train(){for(int i=0;i<N;i++){Train(X[i],Y[i]);}double tmp;GetCurrentOut(tmp);if(tmp < 0.01)return true;elsereturn false;}//获取输入为x时的输出(y)double NeuralKernel::GetValue(double x){for(int i=0;i<MAX;i++)M[i]=Fun(x*aw[i]);double res;res=0.0;for(int i=0;i<MAX;i++)res+=(M[i]*bw[i]);res=Fun(res);return res;}//变换函数double NeuralKernel::Fun(double x){return 1/(1+exp(-x));}//针对训练集中的某一个<x,y>进行训练bool NeuralKernel::Train(double x,double y){double yy,cnt,tmp,tmp1;yy=GetValue(x);cnt=yy*(1-yy)*(y-yy);for(int i=0;i<MAX;i++){tmp=inc*M[i]*cnt;tmp1=inc*M[i]*(1-M[i])*x*bw[i]*cnt;bw[i]+=tmp;aw[i]+=tmp1;}return true;}//保存当前的权值信息到磁盘文件void NeuralKernel::Save(){if(_mkdir("权值") == -1)cout<< "发现'权值'文件夹，正在写入文件......"<<endl;elsecout<<"未发现'权值'文件夹，正在创建之，并将写入文件......"<<endl;char filename[128];sprintf(filename,"权值//%d.txt",(unsigned int)time(NULL));FILE *fp;fp=fopen(filename,"w");if(fp == NULL)return ;int n=MAX;fprintf(fp,"%d/r/n",n);for(int i=0;i<MAX;i++)fprintf(fp,"%.5lf/t",aw[i]);fprintf(fp,"/r/n");for(int i=0;i<MAX;i++)fprintf(fp,"%.5lf/t",bw[i]);fclose(fp);}

测试代码如下：

#include "NeuralKernel.h"int main(){NeuralKernel kernel;vector<double> X,Y,O;int N=30;double PI=3.14159265,start,end;X.resize(N);Y.resize(N);O.resize(N);start=PI/2;end=3*PI/2;//在[start,end]的区间上均匀取N个点作为训练集for(int i=0;i<N;i++){X[i]=(end-start)*i/N+start;Y[i]=(sin(X[i])+1)/2.0;}//设置训练集kernel.SetTeacher(X,Y);int count=0;double E;//设置最大训练次数为5000while(count < 5000){count++;if(kernel.Train())//当总误差小于0.01时，跳出while循环{cout<<"训练完成！"<<endl;O=kernel.GetCurrentOut(E);cout<<count<<" "<<E<<endl;kernel.Save();break;}O=kernel.GetCurrentOut(E);//显示当前的训练次数count及其总误差Ecout<<count<<" "<<E<<endl;}if(count >= 5000){cout<<"训练未完成，真无语呀。。。"<<endl;}//暂停应用程序system("pause");return 0;}