智能算法|BP神经网络(原理及代码实现) C++|神经网络|Python|BP|Python

前言 ??本文主要内容是BP神经网络的Python实现(借助tensorflow库)和C++实现（未借助相关库）
Python实现BP神经网络

import os os.environ['TF_CPP_MIN_LOG_LEVEL'] = '3'#暂时屏蔽警告，只显示error信息 from plugin import * #构建数据 x_data = https://www.it610.com/article/np.arange(-1,1,0.01)[: ,np.newaxis] print("x_data",x_data) noise = np.random.normal(0,0.05,x_data.shape) y_data= https://www.it610.com/article/0.5*(np.sin(x_data)+noise) print("y_data",y_data)#占位符 xs = tf.compat.v1.placeholder(tf.float32,[None,1]) ys =tf.compat.v1.placeholder(tf.float32,[None,1]) h1 = add_layer(xs,1,20,tf.nn.relu) prediction = add_layer(h1,20,1) loss = tf.reduce_mean(tf.reduce_sum(tf.square(ys-prediction), reduction_indices =[1] ) ) train_step = tf.train.GradientDescentOptimizer(0.1).minimize(loss) init = tf.global_variables_initializer()#初始化所有变量 sess = tf.compat.v1.Session()if __name__ == "__main__": sess.run(init) for i in range(10000): sess.run(train_step,feed_dict = {xs:x_data,ys:y_data}) if i %100 ==0: print(sess.run(loss,feed_dict = {xs:x_data,ys:y_data}))

C++实现BP神经网络 BP（Back-Propagating）神经网络的特点是向前传送输入数据，向后反馈误差。理论上，一个三层（输入层，隐含层，输出层）的BP神经网络可以实现任意m维到任意n维的映射。
查看相应代码可访问我的github(https://github.com/YuruTu)，博客主要发挥介绍性的工作，github上更新最新代码
https://github.com/YuruTu/BPNN/blob/master
头文件pch.h

#ifndef PCH_H #define PCH_H #include #include #include #include #include #include #endif //PCH_H

【智能算法|BP神经网络(原理及代码实现)】主函数main.cpp

//作者cclplus //初稿2018/05/01 //如果你认为有必要打赏我，我的支付宝号是707101557@qq.com #include "pch.h" using namespace std; const double pi = atan(1.0) * 4; //BP神经网络结构 struct BPNN { int sample_count; //样本数量 int input_count; //输入向量的维数 int output_count; //输出向量的维数 int hidden_count; //实际使用隐层神经元数量 double study_rate; //学习速率 double precision; //精度控制参数 int loop_count; //循环次数 vector> v; //隐含层权矩阵 vector> w; //输出层权矩阵 }; BPNN CREATE_BPNN(int sc, int ic, int oc, int hc, double sr, double p, int lc); //创建一个BP神经网络 double rand_normal(); //返回一个double类型的随机数 double sigmoid(double net) { return 1.0 / (1 + exp(-net)); } double purelin(double net) { return 1.0 / (1 + exp(-net)); } BPNN train_bp(vector> x, vector> y, BPNN bp); //训练 void use_bp(BPNN bp, vector> inoput); //使用BP神经网络进行前向传导运算 int main() { //样本数目 int sample_count = 100; //输入向量维数 int input_count = 1; //输出向量维数 int output_count = 1; //实际使用隐层神经元数目 int hidden_count = 4; //学习速率 double study_rate = 0.02; //精度控制参数 double precision = 0.001; //循环次数 int loop_count = 10000; int i; double temp, temp1; //训练样本 vector> x; vector> y; vector> input; x.resize(sample_count); for (i = 0; i < sample_count; i++) { x[i].resize(input_count); } y.resize(sample_count); for (i = 0; i < sample_count; i++) { y[i].resize(output_count); } input.resize(sample_count); for (i = 0; i < sample_count; i++) { input[i].resize(input_count); } //自定义输入与输出 for (i = 0; i < sample_count; i++) { temp = (double)i; temp1 = (double)sample_count; x[i][0] = pi / temp1 * temp; input[i][0] = pi / temp1 * temp; y[i][0] = 1.0*sin(x[i][0]); } BPNN bp; bp = CREATE_BPNN(sample_count, input_count, output_count, hidden_count, study_rate, precision, loop_count); bp = train_bp(x, y, bp); use_bp(bp, input); return 0; } //使用BP神经网络进行前向传导运算 void use_bp(BPNN bp, vector> input) { //设置临时变量 double temp; inti, j, k; vector O1; O1.resize(bp.hidden_count); vector> output; output.resize(100); for (i = 0; i < 100; i++) { output[i].resize(bp.output_count); } for (i = 0; i < 100; i++) { for (j = 0; j < bp.hidden_count; j++) { temp = 0; for (k = 0; k < bp.input_count; k++) { temp = temp + input[i][k] * bp.v[k][j]; } O1[j] = sigmoid(temp); } for (j = 0; j < bp.output_count; j++) { temp = 0; for (k = 0; k < bp.hidden_count; k++) { temp = temp + O1[k] * bp.w[k][j]; } output[i][j] = sigmoid(temp); } } for (i = 0; i < 100; i++) { for (j = 0; j < bp.output_count; j++) { printf("%f", output[i][j]); } } printf("\n结束\n"); }//训练一个BP神经网络 BPNN train_bp(vector> x, vector> y, BPNN bp) { double f, a; int hc, sc, lc, ic, oc; f = bp.precision; //精度控制参数 a = bp.study_rate; //学习速率 hc = bp.hidden_count; //隐含层数 sc = bp.sample_count; //训练样本总数 lc = bp.loop_count; //循环次数 ic = bp.input_count; //输入维度 oc = bp.output_count; //输出维度 //修改量矩阵 vector chg_h; //隐层 chg_h.resize(hc); vector chg_o; //输出层 chg_o.resize(oc); vector O1; O1.resize(hc); vector O2; O2.resize(oc); //临时变量 double temp; int i, j, m, n; double mse; //均方误差 double e; //误差 e = f + 1; //保证循环顺利执行 for (n = 0; (e > f) && (n < lc); n++) {//n代表循环次数 e = 0; mse = 0; //全部样本均加入神经网络的训练 for (i = 0; i < sc; i++) { //计算隐层输出向量 for (m = 0; m < hc; m++) { temp = 0; for (j = 0; j < ic; j++) { temp = temp + x[i][j] * bp.v[j][m]; } O1[m] = sigmoid(temp); } //计算输出值 for (m = 0; m < oc; m++) { temp = 0; for (j = 0; j < hc; j++) { temp = temp + O1[j] * bp.w[j][m]; } O2[m] = purelin(temp); } //计算输出层的权重修改 for (j = 0; j < oc; j++) { chg_o[j] = O2[j] * (1 - O2[j])*(y[i][j] - O2[j]); } //计算隐层的权重修改 for (j = 0; j < hc; j++) { temp = 0; for (m = 0; m < oc; m++) { temp = temp + bp.w[j][m] * chg_o[m]; } chg_h[j] = temp * O1[j] * (1 - O1[j]); } //计算误差和均方根误差 for (j = 0; j < oc; j++) { e = e + (y[i][j] - O2[j])*(y[i][j] - O2[j]); mse = mse + y[i][j] * y[i][j]; } //对权值矩阵做出修改 for (j = 0; j < hc; j++) { for (m = 0; m < oc; m++) { bp.w[j][m] = bp.w[j][m] + a * O1[j] * chg_o[m]; } } for (j = 0; j < ic; j++) { for (m = 0; m < hc; m++) { bp.v[j][m] = bp.v[j][m] + a * x[i][j] * chg_h[m]; } } } //每循环一百次输出一次误差 if (n % 100 == 0) { mse = e / mse; printf("误差:%f\n", e); printf("均方根误差:%f\n", mse); printf("当前循环次数:%d\n", n); } } //循环结束，输出最终信息 printf("循环总次数:%d\n", n); printf("调整后的隐层权值矩阵:\n"); for (i = 0; i < ic; i++) { for (j = 0; j < hc; j++) { printf("%f", bp.v[i][j]); } printf("\n"); } printf("调整后的输出层权值矩阵:\n"); for (i = 0; i < hc; i++) { for (j = 0; j < oc; j++) { printf("%f", bp.w[i][j]); } printf("\n"); } printf("神经网络训练结束:\n"); printf("最终误差:%f\n", e); return bp; }//创建一个BP神经网络 BPNN CREATE_BPNN(int sc, int ic, int oc, int hc, double sr, double p, int lc) { BPNN bp; bp.sample_count = sc; bp.input_count = ic; bp.output_count = oc; bp.hidden_count = hc; bp.study_rate = sr; bp.precision = p; bp.loop_count = lc; int i, j; bp.v.resize(ic); //隐含层的权值矩阵，共有input_count行，hidden_count列 for (i = 0; i < ic; i++) { bp.v[i].resize(hc); } //数据的初始化 for (i = 0; i < ic; i++) { for (j = 0; j < hc; j++) { bp.v[i][j] = rand_normal(); } } bp.w.resize(hc); //输出层的权值矩阵，共有hidden_count行，output_count列 for (i = 0; i < hc; i++) { bp.w[i].resize(oc); } for (i = 0; i < hc; i++) { for (j = 0; j < oc; j++) { bp.w[i][j] = rand_normal(); } } return bp; }//返回一个double类型的随机数，这么做的目的是破坏神经网络结构的对称性 //基本原理，参见独立同分布的中心极限定理 double rand_normal() { inti; const int normal_count = 200; //样本数目采用200个 double ccl_num; double ccl_s; double ccl_ar[normal_count]; ccl_num = 0; for (i = 0; i < normal_count; i++) { ccl_ar[i] = rand() % 1000 / (double)1001; ccl_num += ccl_ar[i]; } ccl_num -= (normal_count / 2); //减去0-1均匀分布的均值 ccl_s = 1.0*normal_count / 12.0; //0-1分布的方差为1/12 ccl_s = sqrt(ccl_s); ccl_num /= ccl_s; //此时ccl_num接近标准正态分布的一个子集 ccl_num /= 100; //变为正态分布（0，0.01）的一个子集，论文中有给出证明过程 cout << " 随机值" << ccl_num << endl; return ccl_num; }