简单BP神经网络分类手写数字识别0-9

前言：本人旨在交流代码，细节和原理不清楚的可以留言，以后做完了再整理，现在先放一部分，可以直接使用

1.代码可以直接在c上运行，输入为5*5矩阵，比如数字0：

1 1 1 1 1

1 0 0 0 1

1 0 0 0 1

1 0 0 0 1

1 1 1 1 1

因为训练集合太小，决定用matlab生成大量训练样本，放在后文中。

2.c语言实现代码：（BP推导很简单，不会的自己可以留言，代码中有详细注释)

#include <stdio.h>#include <math.h>#include <stdlib.h>#include <time.h>#define COUNT 50//样本数量#define IN_NUM 25//输入层神经元数量#define OUT_NUM 10//输出层神经元数量#define numHidden 30//隐含层神经元数量double weight_hidden[IN_NUM][numHidden];//输入层到隐含层的权值double bias_hidden[numHidden];//隐含层的阈值double weight_output[numHidden][OUT_NUM];//隐含层到输出层的权值double bias_output[OUT_NUM];//输出层的阈值double learnRate = 0.4;//学习数率double accuracy = 0.001;//最大容许误差0.000001int   maxloopCount = 1000000;//最大学习数率double fnet(double net)//Sigmoid{return 1 / (1 + exp(-net));}double dfnet(double net)//Sigmoid导函数 y = s*（s-1）{return  net * (1 - net);}int InitBP()//得到-1到1随机数{int i, j;srand((unsigned)time(NULL));for (i = 0; i < IN_NUM; i++)for (j = 0; j < numHidden; j++){weight_hidden[i][j] = rand() / (double)(RAND_MAX)-0.5;bias_hidden[j] = rand() / (double)(RAND_MAX)-0.5;}for (i = 0; i < numHidden; i++)for (j = 0; j < OUT_NUM; j++){weight_output[i][j] = rand() / (double)(RAND_MAX)-0.5;bias_output[j] = rand() / (double)(RAND_MAX)-0.5;}return 1;}int TrainBP(float x[COUNT][IN_NUM], float y[COUNT][OUT_NUM]){double delta_hidden[numHidden], delta_output[OUT_NUM];//中间计算量double output_hidden[numHidden], output_output[OUT_NUM];//隐含层输出  输出层输出double temp;//中间累加值double loss;int i, j, k, n;for (n = 0; n < maxloopCount; n++){loss = 0;for (i = 0; i < COUNT; i++)//逐个数据进行计算，整个数据计算一遍后n+1{/*前相传播*///计算隐含层输出for (k = 0; k < numHidden; k++){temp = 0;for (j = 0; j < IN_NUM; j++)temp += x[i][j] * weight_hidden[j][k];output_hidden[k] = fnet(temp + bias_hidden[k]);}//计算输出层输出for (k = 0; k < OUT_NUM; k++){temp = 0;for (j = 0; j < numHidden; j++)temp += output_hidden[j] * weight_output[j][k];output_output[k] = fnet(temp + bias_output[k]);}//计算误差for (j = 0; j < OUT_NUM; j++)loss += 0.5*(y[i][j] - output_output[j])*(y[i][j] - output_output[j]);/*方向传播阶段*///更新输出层的权值for (j = 0; j < OUT_NUM; j++)delta_output[j] = (y[i][j] - output_output[j])*dfnet(output_output[j]);for (j = 0; j < numHidden; j++)for (k = 0; k < OUT_NUM; k++){weight_output[j][k] += learnRate * delta_output[k] * output_hidden[j];}//更新输出层的偏重for (k = 0; k < OUT_NUM; k++)bias_output[k] += learnRate * delta_output[k];//更新隐含层权重for (j = 0; j < numHidden; j++){temp = 0;for (k = 0; k < OUT_NUM; k++)temp += weight_output[j][k] * delta_output[k];delta_hidden[j] = temp * dfnet(output_hidden[j]);}for (j = 0; j<IN_NUM; j++)for (k = 0; k < numHidden; k++)weight_hidden[j][k] += learnRate*delta_hidden[k] * x[i][j];//跟新隐含层偏置for (k = 0; k < numHidden; k++)bias_hidden[k] += learnRate*delta_hidden[k];}if (n % 10 == 0)printf("误差：%f\n", loss);if (loss <= accuracy)break;//达到训练标准，训练提前结束}printf("总的训练次数：%d\n", n);printf("bp网络训练结束！\n");return 1;}int TestBP(){float Input[IN_NUM];//定义输入向量double output_hidden[numHidden];//隐含层输出double output_output[OUT_NUM];//输出层输出double mid= 0;int c;while (1){printf("请输入一个数：\n");int i, j;//输入层for (i = 0; i < IN_NUM; i++){scanf_s("%f", &Input[i]);}//隐含层double temp;for (i = 0; i < numHidden; i++)//输入层神经元与隐含层神经元的连接计算{temp = 0;//中间变量,用于存储隐含层隐含层神经元输出for (j = 0; j < IN_NUM; j++)temp += Input[j] * weight_hidden[j][i];output_hidden[i] = fnet(temp + bias_hidden[i]);}//输出层for (i = 0; i < OUT_NUM; i++){temp = 0;for (j = 0; j < numHidden; j++)temp += output_hidden[j] * weight_output[j][i];output_output[i] = fnet(temp + bias_output[i]);}//输出输出层每一个神经元结果printf("结果为：   ");for (i = 0; i < OUT_NUM; i++)printf("%f ", output_output[i]);for (i = 0; i < OUT_NUM; i++){if (mid < output_output[i]){mid = output_output[i];c = i;}}printf("你输入的数为%d\n", c);printf("\n");}return 1;}int main(){//输入规则：3不允许连排,且输入偏右//x为输入向量，y为输出向量float x[COUNT][IN_NUM] = {  //  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25//------------------------------------0 start----------------------------------------------------//{    1, 1, 1, 1, 1,   1, 0, 0, 0, 1,    1, 0, 0, 0, 1,    1, 0, 0, 0, 1,    1, 1, 1, 1, 1 },       //  1  2  3  4  5{     1, 1, 1, 1, 0,    1, 0, 0, 1, 0,     1, 0, 0, 1, 0,     1, 1, 1, 1, 0,     0, 0, 0, 0, 0 },//  1  2  3  4  5{0, 1, 1, 1, 1,0, 1, 0, 0, 1,0, 1, 0, 0, 1,0, 1, 0, 0, 1,0, 1, 1, 1, 1},//  1  2  3  4  5{1, 1, 1, 1, 0,1, 0, 0, 1, 0,1, 1, 1, 1, 0,0, 0, 0, 0, 0,0, 0, 0, 0, 0},//  1  2  3  4  5{1, 1, 1, 1, 1,1, 0, 0, 0, 1,1, 1, 1, 1, 1,0, 0, 0, 0, 0,0, 0, 0, 0, 0},//------------------------------------0 end------------------------------------------------------------////------------------------------------1 start----------------------------------------------------////  1  2  3  4  5 {1, 0, 0, 0, 0,1, 0, 0, 0, 0,1, 0, 0, 0, 0,1, 0, 0, 0, 0,1, 0, 0, 0, 0},//  1  2  3  4  5{0, 1, 0, 0, 0,0, 1, 0, 0, 0,0, 1, 0, 0, 0,0, 1, 0, 0, 0,0, 1, 0, 0, 0},//  1  2  3  4  5{0, 0, 1, 0, 0,0, 0, 1, 0, 0,0, 0, 1, 0, 0,0, 0, 1, 0, 0,0, 0, 1, 0, 0},//  1  2  3  4  5{0, 0, 0, 1, 0,0, 0, 0, 1, 0,0, 0, 0, 1, 0,0, 0, 0, 1, 0,0, 0, 0, 1, 0},//  1  2  3  4  5{0, 0, 0, 0, 1,0, 0, 0, 0, 1,0, 0, 0, 0, 1,0, 0, 0, 0, 1,0, 0, 0, 0, 1},//------------------------------------1 end------------------------------------------------------------////------------------------------------2 start----------------------------------------------------////  1  2  3  4  5 {1, 1, 1, 1, 1,0, 0, 0, 0, 1,1, 1, 1, 1, 1,1, 0, 0, 0, 0,1, 1, 1, 1, 1},//  1  2  3  4  5{0, 0, 0, 0, 0,1, 1, 1, 1, 1,1, 1, 1, 1, 1,1, 0, 0, 0, 0,1, 1, 1, 1, 1},//  1  2  3  4  5{0, 1, 1, 1, 0,0, 0, 0, 1, 0,0, 1, 1, 1, 0,0, 1, 0, 0, 0,0, 1, 1, 1, 0},//  1  2  3  4  5{1, 1, 1, 1, 0,0, 0, 0, 1, 0,1, 1, 1, 1, 0,1, 0, 0, 0, 0,1, 1, 1, 1, 0},//  1  2  3  4  5{0, 1, 1, 1, 1,0, 0, 0, 0, 1,0, 1, 1, 1, 1,0, 1, 0, 0, 0,0, 1, 1, 1, 1},//------------------------------------2 end------------------------------------------------------------////------------------------------------3 start----------------------------------------------------////  1  2  3  4  5 {1, 1, 1, 1, 1,0, 0, 0, 0, 1,1, 1, 1, 1, 1,0, 0, 0, 0, 1,1, 1, 1, 1, 1},//  1  2  3  4  5{1, 1, 1, 1, 0,0, 0, 0, 1, 0,1, 1, 1, 1, 0,0, 0, 0, 1, 0,1, 1, 1, 1, 0},//  1  2  3  4  5{1, 1, 1, 0, 0,0, 0, 1, 0, 0,1, 1, 1, 0, 0,0, 0, 1, 0, 0,1, 1, 1, 0, 0},//  1  2  3  4  5{1, 1, 1, 1, 1,1, 1, 1, 1, 1,0, 0, 0, 0, 1,0, 0, 0, 0, 1,1, 1, 1, 1, 1},//  1  2  3  4  5{0, 0, 1, 1, 1,0, 0, 1, 1, 1,0, 0, 0, 0, 1,0, 0, 1, 1, 1,0, 0, 0, 0, 0},//------------------------------------3 end------------------------------------------------------------////------------------------------------4 start----------------------------------------------------////  1  2  3  4  5 {1, 1, 0, 0, 0,1, 1, 0, 0, 0,1, 1, 0, 0, 0,1, 1, 1, 1, 1,0, 1, 0, 0, 0},//  1  2  3  4  5{1, 0, 1, 0, 0,1, 0, 1, 0, 0,1, 1, 1, 1, 1,0, 0, 1, 0, 0,0, 0, 1, 0, 0},//  1  2  3  4  5{1, 0, 0, 1, 0,1, 0, 0, 1, 0,1, 1, 1, 1, 1,0, 0, 0, 1, 0,0, 0, 0, 1, 0},//  1  2  3  4  5{1, 0, 0, 0, 1,1, 0, 0, 0, 1,1, 0, 0, 0, 1,1, 1, 1, 1, 1,0, 0, 0, 0, 1},//  1  2  3  4  5{1, 0, 1, 0, 0,1, 0, 1, 0, 0,1, 1, 1, 1, 1,0, 0, 1, 0, 0,0, 0, 1, 0, 0},//------------------------------------4 end------------------------------------------------------------////------------------------------------5 start----------------------------------------------------////  1  2  3  4  5 {1, 1, 1, 1, 1,1, 0, 0, 0, 0,1, 1, 1, 1, 1,0, 0, 0, 0, 1,1, 1, 1, 1, 1},//  1  2  3  4  5{1, 1, 1, 1, 0,1, 0, 0, 0, 0,1, 1, 1, 1, 0,0, 0, 0, 1, 0,1, 1, 1, 1, 0},//  1  2  3  4  5{1, 1, 1, 0, 0,1, 0, 0, 0, 0,1, 1, 1, 0, 0,1, 1, 1, 0, 0,0, 0, 0, 0, 0},//  1  2  3  4  5{1, 1, 1, 0, 0,1, 0, 0, 0, 0,1, 1, 1, 0, 0,0, 0, 1, 0, 0,1, 1, 1, 0, 0},//  1  2  3  4  5{0, 1, 1, 1, 0,0, 1, 0, 0, 0,0, 1, 1, 1, 0,0, 0, 0, 1, 0,0, 1, 1, 1, 0},//------------------------------------5 end------------------------------------------------------------////------------------------------------6 start----------------------------------------------------////  1  2  3  4  5 {1, 1, 1, 1, 1,1, 0, 0, 0, 0,1, 1, 1, 1, 1,1, 0, 0, 0, 1,1, 1, 1, 1, 1},//  1  2  3  4  5{1, 0, 0, 0, 0,1, 0, 0, 0, 0,1, 1, 1, 1, 1,1, 0, 0, 0, 1,1, 1, 1, 1, 1},//  1  2  3  4  5{1, 1, 1, 0, 0,1, 0, 0, 0, 0,1, 1, 1, 0, 0,1, 0, 1, 0, 0,1, 1, 1, 0, 0},//  1  2  3  4  5{0, 0, 1, 1, 1,0, 0, 1, 0, 0,0, 0, 1, 1, 1,0, 0, 1, 1, 1,0, 0, 0, 0, 0},//  1  2  3  4  5{0, 1, 0, 0, 0,0, 1, 0, 0, 0,0, 1, 1, 1, 1,0, 1, 0, 0, 1,0, 1, 1, 1, 1},//------------------------------------6 end------------------------------------------------------------////------------------------------------7 start----------------------------------------------------////  1  2  3  4  5 {1, 1, 1, 1, 1,0, 0, 0, 0, 1,0, 0, 0, 0, 1,0, 0, 0, 0, 1,0, 0, 0, 0, 1},//  1  2  3  4  5{0, 1, 1, 1, 1,0, 0, 0, 0, 1,0, 0, 0, 0, 1,0, 0, 0, 0, 1,0, 0, 0, 0, 0},//  1  2  3  4  5{0, 0, 0, 0, 0,0, 1, 1, 1, 1,0, 0, 0, 0, 1,0, 0, 0, 0, 1,0, 0, 0, 0, 1},//  1  2  3  4  5{0, 0, 0, 0, 0,0, 1, 1, 1, 0,0, 0, 0, 1, 0,0, 0, 0, 1, 0,0, 0, 0, 1, 0},//  1  2  3  4  5{0, 0, 0, 0, 0,0, 0, 0, 0, 0,1, 1, 1, 0, 0,0, 0, 1, 0, 0,0, 0, 1, 0, 0},//------------------------------------7 end------------------------------------------------------------////------------------------------------8 start----------------------------------------------------////  1  2  3  4  5 {1, 1, 1, 1, 1,1, 0, 0, 0, 1,1, 1, 1, 1, 1,1, 0, 0, 0, 1,1, 1, 1, 1, 1},//  1  2  3  4  5{1, 1, 1, 0, 0,1, 0, 1, 0, 0,1, 1, 1, 0, 0,1, 0, 1, 0, 0,1, 1, 1, 0, 0},//  1  2  3  4  5{0, 0, 1, 1, 1,0, 0, 1, 0, 1,0, 0, 1, 1, 1,0, 0, 1, 0, 1,0, 0, 1, 1, 1},//  1  2  3  4  5{0, 1, 1, 1, 0,0, 1, 0, 1, 0,0, 1, 1, 1, 0,0, 1, 1, 1, 0,0, 0, 0, 0, 0},//  1  2  3  4  5{0, 1, 1, 1, 1,0, 1, 0, 0, 1,0, 1, 1, 1, 1,0, 1, 0, 0, 1,0, 1, 1, 1, 1},//------------------------------------8 end------------------------------------------------------------////------------------------------------9 start----------------------------------------------------////  1  2  3  4  5 {1, 1, 1, 1, 1,1, 0, 0, 0, 1,1, 1, 1, 1, 1,0, 0, 0, 0, 1,0, 0, 0, 0, 1},//  1  2  3  4  5{1, 1, 1, 0, 0,1, 0, 1, 0, 0,1, 1, 1, 0, 0,0, 0, 1, 0, 0,0, 0, 1, 0, 0},//  1  2  3  4  5{0, 0, 1, 1, 1,0, 0, 1, 0, 1,0, 0, 1, 1, 1,0, 0, 0, 0, 1,0, 0, 0, 0, 1},//  1  2  3  4  5{0, 0, 0, 0, 0,1, 1, 1, 1, 0,1, 0, 0, 1, 0,1, 1, 1, 1, 0,0, 0, 0, 1, 0},//  1  2  3  4  5{0, 1, 1, 1, 0,0, 1, 0, 1, 0,0, 1, 1, 1, 0,0, 0, 0, 1, 0,0, 0, 0, 1, 0},//------------------------------------9 end------------------------------------------------------------//};float y[COUNT][OUT_NUM] = {{ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 },{ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 },{ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 },{ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 },{ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 },//0{ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 },{ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 },{ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 },{ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 },{ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 },//1{ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 },{ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 },{ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 },{ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 },{ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 },//2{ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 },{ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 },{ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 },{ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 },{ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 },//3{ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 },{ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 },{ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 },{ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 },{ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 },//4{ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 },{ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 },{ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 },{ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 },{ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 },//5{ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 },{ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 },{ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 },{ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 },{ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 },//6{ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 },{ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 },{ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 },{ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 },{ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 },//7{ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 },{ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 },{ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 },{ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 },{ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 },//8{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 },{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 },{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 },{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 },{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 },//9};InitBP();//初始化BP网络TrainBP(x, y);//训练BPTestBP();//测试BPreturn 1;}

c语言程序运行结果：

很明显，对于输入的矩阵完美判别（受到训练集合大小和图像像素的影响，对于不规则输入有很大误差）

3.训练集合太小，所以我又研究了下matlab手写输入画板，在matlab下新建图形界面，传送门：http://blog.sina.com.cn/s/blog_86a4e34a0102vxra.html，参考了这个代码。

matlab手写画板.m文件几个重要函数在传送门直接可以用，使用效果如下：

这是打开的matlab手写输入板，自己写的1，保存为bmp图像，保存按钮的代码如下：（传送门没有）

% --- Executes on button press in pushbutton2.function pushbutton2_Callback(hObject, eventdata, handles)% hObject    handle to pushbutton2 (see GCBO)% eventdata  reserved - to be defined in a future version of MATLAB% handles    structure with handles and user data (see GUIDATA)h=getframe(handles.axes1);imwrite(h.cdata,'output.bmp','bmp');cla(handles.axes1);

4.对于保存的图像生成二进制，matlab代码如下：

clc;  clear;  filename = 'output.bmp';  %读出源文件imfinfo(filename) % 查看图像文件信息  imgRgb = imread(filename); % 读入一幅彩色图像  imshow(imgRgb); % 显示彩色图像    imgGray = rgb2gray(imgRgb); % 转为灰度图像  figure % 打开一个新的窗口显示灰度图像  imshow(imgGray); % 显示转化后的灰度图像  % imwrite(imgGray, 'gray.jpg'); % 将灰度图像保存到图像文件    thresh = graythresh(imgGray);     %自动确定二值化阈值  I = im2bw(imgGray,thresh);       %对图像二值化  ci=imresize(I,[16,16]); %把ai转成256x256的大小ti =~ci;%对图像取反figureimshow(ti)%画取反后的图figureimshow(ci)%画压缩后的二进制figure  imshow(I); %画二进制图

结果如下：

左到右依次为原图、灰度图、压缩后的二进制图，原本二进制图，我们需要的数据就存储在二进制图的数组里面16*16大小，可以弄大一点，这样对于输入的判断会更准。

本文缺陷：1.c语言中读入训练集合和测试集合应改为文件流操作，这样对于大量数据文件的训练和测试会很方便，matlab 生成图像文件和二进制文件可以直接改为文件操作，时间有限感兴趣的可以基于我的demo改，希望能共同学习共同进步！！！

结束语：c语言实现只是我测试的一个东西，我的目的是用ASIC集成电路实现，下一步将在fpga使用verilog语言实现这个手写输入识别！敬请关注！

文中多有瑕疵和漏洞，欢迎指教！