机器学习--BP神经网络的C++实现

激活函数:Sigmoid

使用的是周志华老师的《机器学习》一书上的更新公式。

一共有三层，第一层是三维的，第二层是4维，输出层是1维。

#include <iostream>
#include <cstdlib>
#include <ctime>
#include <cmath>
using namespace std;

#define  innode 3  //输入结点数  
#define  outnode 1 //输出结点数  
#define  trainsample 8//BP训练样本数 
#define  INF 99999999 //定义无穷大

//初始化权值
void initialValue(double **weight1,double **weight2,double *bias1,double *bias2,int n1,int n2,int n3)
{
    for(int i=; i<n1; i++)
    {
        for(int j=; j<n2; j++)
        {
            //用来设置rand()产生随机数时的随机数种子。参数seed必须是个整数，如果每次seed都设相同值，rand()所产生的随机数值每次就会一样
            srand(time(NULL));
            weight1[i][j]=rand()%/();
        }
    }
    for(int i=; i<n2; i++)
    {
        for(int j=; j<n3; j++)
        {
            srand(time(NULL));
            weight2[i][j]=rand()%/();
        }
    }
    for(int i=; i<n2; i++)
    {
        srand(time(NULL));
        bias1[i]=rand()%/();
    }
    for(int i=; i<n3; i++)
    {
        srand(time(NULL));
        bias2[i]=rand()%/();
    }
}

double sigmoid(double x)
{
    return /(+exp(-x));
}

//计算样本实际输出
void  computeY(double **weight1,double **weight2,double *bias1,double *bias2,int n1,int n2,int n3,double X[innode],double predictY[outnode],double *hideY)
{
    double sum=;

    //计算隐层输出
    for(int i=; i<n2; i++)
    {
        for(int j=; j<n1; j++)
        {
            sum += weight1[j][i]*X[j];
        }
        sum=sigmoid(sum-bias1[i]);
        hideY[i]=sum;
    }
    sum=;
    //计算最后一层输出
    for(int i=; i<n3; i++)
    {
        for(int j=; j<n2; j++)
        {
            sum += weight2[j][i]*hideY[i];
        }
        sum=sigmoid(sum-bias2[i]);
        predictY[i]=sum;
    }
}
//计算输出神经元的梯度
void computeOutputDY(int n3,double predictY[outnode],double Y[outnode],double *outputDweight)
{
    for(int i=; i<n3; i++)
    {
        outputDweight[i]=predictY[i]*(-predictY[i])*(Y[i]-predictY[i]);
    }

}

//计算隐藏神经元的梯度
void computeHideDY(double **weight2,int n2,int n3,double *hideY,double *outputDweight,double *hideDweight)
{
    for(int i=; i<n2; i++)
    {
        double sum=;
        for(int j=; j<n3; j++)
        {
            sum+=weight2[i][j]*outputDweight[j];
        }
        hideDweight[i]=hideY[i]*(-hideY[i])*sum;
    }
}

//更新权值
void updateWeight(double **weight1,double **weight2,double *bias1,double *bias2,int n1,int n2,int n3,double X[innode],double *hideY,double *outputDweight,double *hideDweight,double ratio)
{
    for(int i=; i<n1; i++)
    {
        for(int j=; j<n2; j++)
        {
            weight1[i][j]+=ratio*hideDweight[j]*X[i];
        }
    }
    for(int i=; i<n2; i++)
    {
        for(int j=; j<n3; j++)
        {
            weight2[i][j]+=ratio*outputDweight[j]*hideY[i];
        }
    }
    for(int i=; i<n2; i++)
    {
        bias1[i]-=ratio*hideDweight[i];
    }
    for(int i=; i<n3; i++)
    {
        bias2[i]-=ratio*outputDweight[i];
    }
}
//计算均方误差
double computeError(double predictY[outnode],double Y[outnode],int n)
{
    double error=;
    for(int i=; i<n; i++)
    {
        error += ((predictY[i]-Y[i])*(predictY[i]-Y[i]));
    }
    return error;
}
int main()
{
    //三层神经网络，各层的维度
    int n1=,n2=,n3=;
    cout<<"输入各层的维度：";
    cin>>n1>>n2>>n3;

    //输入层与隐层的连接权n1xn2，隐层与输出层的连接权n2xn3
    double **weight1=new double*[n1];
    for(int i=;i<n1;i++)
        weight1[i]=new double[n2];

    double **weight2=new double*[n2];
    for(int i=;i<n2;i++)
        weight2[i]=new double[n3];

    //隐藏层的梯度项，输出层的梯度项
    double *outputDweight = new double[n3];
    double *hideDweight = new double[n2];

    //隐层的偏置，输出层的偏置
    double *bias1 = new double[n2];
    double *bias2 = new double[n3];

    //输入样本  n1=3,n3=1
    double X[trainsample][innode]= {{,,},{,,},{,,},{,,},{,,},{,,},{,,},{,,}};  
    //期望输出样本  
    double Y[trainsample][outnode]={{},{},{},{},{},{},{},{}};  

    //实际输出样本
    double **predictY=new double*[trainsample];
    for(int i=;i<trainsample;i++)
        predictY[i]=new double[outnode];

    //隐层输出样本
    double *hideY=new double[n2];

    //权值，偏置初始化
    initialValue(weight1,weight2,bias1,bias2,n1,n2,n3);

    double error=INF;
    //学习率
    double ratio=;

    while(error>)
    {
        error=;
        for(int i=; i<trainsample; i++)
        {
            //计算输出层的值
            computeY(weight1,weight2,bias1,bias2,n1,n2,n3,X[i],predictY[i],hideY);
            //计算输出层的梯度项
            computeOutputDY(n3,predictY[i],Y[i],outputDweight);
            //计算隐层的梯度项
            computeHideDY(weight2,n2,n3,hideY,outputDweight,hideDweight);
            //更新权值
            updateWeight(weight1,weight2,bias1,bias2,n1,n2,n3,X[i],hideY,outputDweight,hideDweight,ratio);
            //计算均方误差
            error += computeError(predictY[i],Y[i],outnode);
        }
        error=*error;
    }

    //输出网络的输出与实际输出的对应
    for(int i=; i<trainsample; i++)
    {
        for(int j=; j<outnode; j++)
        {
            cout<<"predictY[i][j]::"<<predictY[i][j]<<"----"<<"Y[i][j]::"<<Y[i][j]<<endl;
        }
    }

    //释放空间
    for(int i=;i<n1;i++)
    {
        delete []  weight1[i];  
    }
    for(int i=;i<n2;i++)
    {
        delete []  weight2[i];
    }

    delete [] weight1;
    delete [] weight2;
    delete [] bias1;
    delete [] bias2;
}