简单BP算法实现

算法流程

 Matlab实现

clear all;
%step1
xp=[1,3];
yp=[0.95,0.35];
err_max=0.01;
iterate=0;
xp_tmp=[1 1 1];
step=0.1;
nums=1;
result=[];
%初始权值
w1_1=-1 + (1+1)*rand(1,3);
w1_2=-1 + (1+1)*rand(1,3);
w2_1=-1 + (1+1)*rand(1,3);
w2_2=-1 + (1+1)*rand(1,3);
xp_tmp(1:2)=xp(1:2);
%step2
while(1)
    nums=nums+1;
    net1_1=w1_1*xp_tmp';
    net1_2=w1_2*xp_tmp';
    o1=1/(1+exp(-net1_1));
    o2=1/(1+exp(-net1_2));
    tmp2=[o1 o2 1];
    net2_1=w2_1*tmp2';
    net2_2=w2_2*tmp2';
    y1=1/(1+exp(-net2_1));
    y2=1/(1+exp(-net2_2));
    %step3
    e_tmp=((y1-yp(1))^2+(y2-yp(2))^2)/2;
    result=[result e_tmp];
    if(e_tmp>err_max)
        %step4
        delt1_2=(yp(1)-y1)*y1*(1-y1);
        delt2_2=(yp(2)-y2)*y2*(1-y2);
        delt1_1=(delt1_2*w2_1(1)+delt2_2*w2_2(1))*o1*(1-o1);
        delt2_1=(delt1_2*w2_1(2)+delt2_2*w2_2(2))*o2*(1-o2);
        %step5
        w1_1(1)=w1_1(1)+step*delt1_1*xp(1);
        w1_1(2)=w1_1(2)+step*delt1_1*xp(2);
        w1_1(3)=w1_1(3)+step*delt1_1*1;

        w1_2(1)=w1_2(1)+step*delt2_1*xp(1);
        w1_2(2)=w1_2(2)+step*delt2_1*xp(2);
        w1_2(3)=w1_2(3)+step*delt2_1*1;

        w2_1(1)=w2_1(1)+step*delt1_2*o1;
        w2_1(2)=w2_1(2)+step*delt1_2*o2;
        w2_1(3)=w2_1(3)+step*delt1_2*1;

        w2_2(1)=w2_2(1)+step*delt2_2*o1;
        w2_2(2)=w2_2(2)+step*delt2_2*o2;
        w2_2(3)=w2_2(3)+step*delt2_2*1;
    else
        break;
    end
end
plot(result);xlabel(['steps:',num2str(nums)]);
ylabel('Mean squared error');

结果分析 

VC++实现 

#include <iostream>
#include <algorithm>
#include <vector>
#include <time.h>
#include <string>
#include<cmath>
using namespace std;
int main()
{
	srand((unsigned int)time(NULL));
	vector<int> xp = { 1,3 };
	vector<double> yp = { 0.95,0.35 };
	float err_max = 0.01;
	int iterator = 0;
	vector<int> xp_tmp = { 0,0,1 };
	float step = 0.1;
	int nums = 1;
	vector<double> w11, w12, w21, w22, tmp2, result;
	//初始权值随机
	double r;
	for (int i = 0; i<3; i++)
	{
		r = rand() % 20000 - 10000;
		w11.push_back(r / 10000.0);
		r = rand() % 20000 - 10000;
		w12.push_back(r / 10000.0);
		r = rand() % 20000 - 10000;
		w21.push_back(r / 10000.0);
		r = rand() % 20000 - 10000;
		w22.push_back(r / 10000.0);
	}
	xp_tmp[0] = xp[0];
	xp_tmp[1] = xp[1];
	//step2
	
	while (1)
	{
		double net11 = 0.0, net12 = 0.0, net21 = 0.0, net22 = 0.0,
			o1 = 0.0, o2 = 0.0, y1 = 0.0, y2 = 0.0, e_tmp = 0.0,
			del12 = 0.0, del22 = 0.0, del11 = 0.0, del21 = 0.0;
		nums++;
		for (int i = 0; i<3; i++)
		{
			net11 += w11[i] * xp_tmp[i];
			net12 += w12[i] * xp_tmp[i];
		}
		o1 = 1 / (1 + exp(-net11));
		o2 = 1 / (1 + exp(-net12));
		tmp2.push_back(o1);
		tmp2.push_back(o2);
		tmp2.push_back(1.0);
		for (int i = 0; i<3; i++)
		{
			net21 += w21[i] * tmp2[i];
			net22 += w22[i] * tmp2[i];
		}
		y1 = 1 / (1 + exp(-net21));
		y2 = 1 / (1 + exp(-net22));
		//step3
		e_tmp = 0.5*((y1 - yp[0])*(y1 - yp[0]) + (y2 - yp[1])*(y2 - yp[1]));
		result.push_back(e_tmp);
		if (e_tmp>err_max)
		{
			//step4
			del12 = (yp[0] - y1)*y1*(1 - y1);
			del22 = (yp[1] - y2)*y2*(1 - y2);
			del11 = (del12*w21[0] + del22*w22[0])*o1*(1 - o1);
			del21 = (del12*w21[1] + del22*w22[1])*o2*(1 - o2);

			//step5
			w11[0] += step*del11*xp[0];
			w11[1] += step*del11*xp[1];
			w11[2] += step*del11 * 1;

			w12[0] += step*del21*xp[0];
			w12[1] += step*del21*xp[1];
			w12[2] += step*del21 * 1;

			w21[0] += step*del12*o1;
			w21[1] += step*del12*o2;
			w21[2] += step*del12 * 1;

			w22[0] += step*del22*o1;
			w22[0] += step*del22*o2;
			w22[0] += step*del22 * 1;
		}
		else
		{
			cout << "y1,y2:" << y1 << "," << y2 << endl;
			break;
		}

	}
	cout << "steps:" << nums << endl;
	cout << "*********************************" << endl;
	cout << "mean squared error" << endl;
	for (int i = 0; i < result.size(); i++)
	{
		cout << result[i] << endl;
	}
	cout << "***********************************" << endl;
	cout << "w11:" << endl;
	for (int i = 0; i < w11.size(); i++)
	{
		cout << w11[i] <<" ";
	}
	cout << endl;
	cout << "w12:" << endl;
	for (int i = 0; i < w12.size(); i++)
	{
		cout << w12[i] <<" ";
	}
	cout << endl;
	cout << "w21:" << endl;
	for (int i = 0; i < w21.size(); i++)
	{
		cout << w21[i] <<" ";
	}
	cout << endl;
	cout << "w22:" << endl;
	for (int i = 0; i < w22.size(); i++)
	{
		cout << w22[i] <<" ";
	}
	cout << endl;
	system("pause");
	return 0;
}

输出结果