以上仅给出了代码。具体BP实现原理及神经网络相关知识请见：神经网络和反向传播算法推导
首先是前向传播的计算：
输入:
首先为正整数 n、m、p、t,分别代表特征个数、训练样本个数、隐藏层神经元个数、输出
层神经元个数。其中(1<n<=100,1<m<=1000, 1<p<=100, 1<t<=10)。
随后为 m 行,每行有 n+1 个整数。每行代表一个样本中的 n 个特征值 (x 1 , x 2 ,..., x n ) 与样本的
实际观测结果 y。特征值的取值范围是实数范围,实际观测结果为(1-t 的正整数)。
最后为 2 组特征权值矩阵初始化值。
第一组为输入层与隐藏层特征权值矩阵,矩阵大小为 p*(n+1)。
第二组为隐藏层与输出层特征权值矩阵,矩阵大小为 t*(p+1)。
输出:
包括三部分:
第一行为 1 个浮点数,是神经网络使用初始特征权值矩阵计算出的代价值 J。
然后是 m 行,每行为 p 个浮点数,神经网络隐藏层的输出(不算偏移 bias)。
最后是 m 行,每行为 t 个浮点数,神经网络输出层的输出(不算偏移 bias)。
Sample Input1:
3 3 5 3
0.084147 0.090930 0.014112 3
0.090930 0.065699 -0.053657 2
2 3 4 1
0.084147 -0.027942 -0.099999 -0.028790
0.090930 0.065699 -0.053657 -0.096140
0.014112 0.098936 0.042017 -0.075099
-0.075680 0.041212 0.099061 0.014988
-0.095892 -0.054402 0.065029 0.091295
0.084147 -0.075680 0.065699 -0.054402 0.042017 -0.028790
0.090930 -0.095892 0.098936 -0.099999 0.099061 -0.096140
0.014112 -0.027942 0.041212 -0.053657 0.065029 -0.075099
Sample Output1:
2.0946610.518066 0.522540 0.506299 0.484257 0.476700
0.519136 0.524614 0.507474 0.483449 0.474655
0.404465 0.419895 0.509409 0.589979 0.587968
0.514583 0.511113 0.497424
0.514587 0.511139 0.497447
0.515313 0.511164 0.496748
此处需要补充说明的是这里计算的只是单层神经网络并且在lable原本的值是3,2,1代表的是第一次输出第三个输出单元输出为1，第二次输出第二个输出单元输出为1...
python代码如下：
#coding=utf-8
from numpy import *
#from math import *
from numpy.distutils.core import numpy_cmdclass
f=open( r'test')
input=[]
#数据预处理，把文件数据转换
for each in f:
input.append(each.strip().split())
n,m,p,t=input[0]
sample=input[1:int(n)+1]
w_in_hidden=input[int(n)+1:int(n)+6]
w_hidden_out=input[int(n)+6:]
feature=[]#特征矩阵
lable=[]#标记
for each in sample:
feature.append(each[:-1])
lable.append(each[-1])
#将list转化成矩阵
feature=mat(feature)
lable=mat(lable)
w_in_hidden=mat(w_in_hidden)#隐藏层与输入层的权值矩阵
w_hidden_out=mat(w_hidden_out)#隐藏层与输出层的权值矩阵
#逆置
feature=feature.T
zero=mat(ones(feature.shape[0]))
feature=row_stack((zero,feature))
#将第0行加入矩阵，属矩阵拼接问题
feature=feature.astype(dtype=float)
#生成新的矩阵，并改变矩阵内部数据类型，以前是str型的
w_in_hidden=w_in_hidden.astype(dtype=float)
lable=lable.astype(dtype=float)
w_hidden_out=w_hidden_out.astype(dtype=float)
hidden_output=dot(w_in_hidden,feature)
hidden_output=hidden_output.T
#此处exp是numpy里面自带的求矩阵指数的函数
hidden_output=1/(1+exp(-1*hidden_output))
print hidden_output#隐藏层的输出
hidden_output=hidden_output.T
zero=mat(ones(hidden_output.shape[1]))
hidden_output=row_stack((zero,hidden_output))
output=dot(w_hidden_out,hidden_output)
output=output.T
output=1/(1+exp(-1*output))
print output#输出层的输出
#lable原本的值是3,2,1代表的是第一次输出第三个输出单元输出为1，第二次输出第二个输出单元输出为1...
lable=mat([[0,0,1],[0,1,0],[1,0,0]])
lable=lable.T
output=output.tolist()#将矩阵转化回list
lable=lable.tolist()
sum=0.0
#计算误差，其实也可以直接用矩阵计算，问题在于本人没有找到求矩阵对角线和的函数，且做一标记，找到补上
for i in range (len(output)):
for j in range (len(output[0])):
sum+=math.log(output[i][j])*-lable[i][j]-math.log(1-output[i][j])*(1-lable[i][j])
print sum/3
此处输出顺序不对，请忽略这种小问题～～
输出结果如下：
C代码如下：（C代码）
#include <stdio.h>
#include <math.h>
#define MAX_SAMPLE_NUMBER 1024
#define MAX_FEATURE_DIMENSION 128
#define MAX_LABEL_NUMBER 12
double sigmoid(double z){
return 1 / (1 + exp(-z));
}
double hypothesis(double x[], double theta[], int feature_number){
//此处的hypothesis计算的是某个神经元的输出
double h = 0;
for (int i = 0; i <= feature_number; i++){
h += x[i] * theta[i];
}
return sigmoid(h);
}
void forward_propagation(double a[],
int feature_number,
double W[][MAX_FEATURE_DIMENSION],
int neuron_num,
double output[]){
for (int i = 0; i < neuron_num; i++){
output[i+1] = hypothesis(a, W[i], feature_number);
//w[i]对应着第i个输出神经元的上一层权值
}
}
double compute_cost(double X[][MAX_FEATURE_DIMENSION],
int y[],
int feature_number,
int sample_number,
double W1[][MAX_FEATURE_DIMENSION],
int hidden_layer_size,
double W2[][MAX_FEATURE_DIMENSION],
int label_num,
double a2[][MAX_FEATURE_DIMENSION],
double a3[][MAX_FEATURE_DIMENSION]){
//a2为隐藏层输出a3为输出层输出w1，w2相同
double sum = 0;
for (int i = 0; i < sample_number; i++){
X[i][0] = 1;
forward_propagation(X[i], feature_number, W1, hidden_layer_size, a2[i]);
a2[i][0] = 1;
forward_propagation(a2[i], hidden_layer_size, W2, label_num, a3[i]);
double yy[MAX_LABEL_NUMBER] = {0};
yy[y[i]] = 1;
for (int j = 1; j <= label_num; j++){
sum += -yy[j] * log(a3[i][j]) - (1 - yy[j]) * log(1 - a3[i][j]);
}
}
return sum / sample_number;
}
double X[MAX_SAMPLE_NUMBER][MAX_FEATURE_DIMENSION];
int y[MAX_SAMPLE_NUMBER];
double W1[MAX_FEATURE_DIMENSION][MAX_FEATURE_DIMENSION];
double W2[MAX_FEATURE_DIMENSION][MAX_FEATURE_DIMENSION];
double a2[MAX_SAMPLE_NUMBER][MAX_FEATURE_DIMENSION];
double a3[MAX_SAMPLE_NUMBER][MAX_FEATURE_DIMENSION];
int main(){
int feature_number;
int sample_number;
int hidden_layer_size;
int label_num;
scanf("%d %d %d %d", &feature_number, &sample_number, &hidden_layer_size, &label_num);
for (int i = 0; i < sample_number; i++){
for (int j = 1; j <= feature_number; j++){
scanf("%lf", &X[i][j]);
}
scanf("%d", &y[i]);
}
for (int i = 0; i < hidden_layer_size; i++){
for (int j = 0; j <= feature_number; j++){
scanf("%lf", &W1[i][j]);
}
}
for (int i = 0; i < label_num; i++){
for (int j = 0; j <= hidden_layer_size; j++){
scanf("%lf", &W2[i][j]);
}
}
double J = compute_cost(X, y, feature_number, sample_number,
W1, hidden_layer_size, W2, label_num, a2, a3);
printf("%lf\n", J);
for (int i = 0; i < sample_number; i++){
for (int j = 1; j < hidden_layer_size; j++){
printf("%lf ", a2[i][j]);
}
printf("%lf\n", a2[i][hidden_layer_size]);
}
for (int i = 0; i < sample_number; i++){
for (int j = 1; j < label_num; j++){
printf("%lf ", a3[i][j]);
}
printf("%lf\n", a3[i][label_num]);
}
return 0;
}
结果如下：
关于BP算法，没有找到合适的测试样例，此处仅仅给出了C++版本代码和自测数据，无验证集
C++代码：
#include <stdio.h>
#include <math.h>
double sigmoid(double z){
return 1 / (1 + exp(-z));
}
double hypothesis(double x[], double theta[], int feature_number){
double h = 0;
for (int i = 0; i <= feature_number; i++){
h += x[i] * theta[i];
}
return h;
}
#define MAX_FEATURE_DIMENSION 128
#define MAX_LABEL_NUMBER 12
void forward_propagation(double input[],
int feature_number,
double W[][MAX_FEATURE_DIMENSION],
int neuron_num,
double z[],
double a[]){
for (int i = 0; i < neuron_num; i++){
z[i+1] = hypothesis(input, W[i], feature_number);
a[i+1] = sigmoid(z[i+1]);
//加1的原因是第一个要留作补充的神经元
}
}
double sigmoid_gradient(double z){
return sigmoid(z) * (1 - sigmoid(z));
//对sigmoid函数求导可以化成如此形式，要注意的是z才是自变量
}
void compute_layer_error(double layer_error[],
double W[][MAX_FEATURE_DIMENSION],
int neuron_num,
int feature_number,
double next_layer_error[],
double z[]){
//此处计算的是theta(l)具体见上一篇博文
for (int i = 1; i <= feature_number; i++){
for (int j = 0; j < neuron_num; j++){
layer_error[i] += W[j][i] * next_layer_error[j + 1];//next_layer_error[j + 1]=theta(l+1)
}
}
for (int i = 1; i <=feature_number; i++){
layer_error[i] = layer_error[i] * sigmoid_gradient(z[i]);
}
}
void accumulate_gradient(double sum[][MAX_FEATURE_DIMENSION],
double layer_error[],
int neuron_num,
int feature_number,
double a[]){
//计算误差总和
for (int i = 0; i < neuron_num; i++){
for (int j = 0; j <= feature_number; j++){
sum[i][j] += layer_error[i+1] * a[j];
}
}
}
void compute_gradient(double X[][MAX_FEATURE_DIMENSION],
int y[],
int feature_number,
int sample_number,
double W1[][MAX_FEATURE_DIMENSION],
int hidden_layer_size,
double W2[][MAX_FEATURE_DIMENSION],
int label_num,
double w1_grad[][MAX_FEATURE_DIMENSION],
double w2_grad[][MAX_FEATURE_DIMENSION]){
double grad1_sum[MAX_FEATURE_DIMENSION][MAX_FEATURE_DIMENSION] = {0};
double grad2_sum[MAX_FEATURE_DIMENSION][MAX_FEATURE_DIMENSION] = {0};
for (int i = 0; i < sample_number; i++){
X[i][0] = 1;
double z2[MAX_FEATURE_DIMENSION] = {0, 0};
double a2[MAX_FEATURE_DIMENSION] = {1, 0};
forward_propagation(X[i], feature_number, W1, hidden_layer_size, z2, a2);
double z3[MAX_FEATURE_DIMENSION] = {0};
double a3[MAX_FEATURE_DIMENSION] = {0};
forward_propagation(a2, hidden_layer_size, W2, label_num, z3, a3);
double yy[MAX_LABEL_NUMBER] = {0};
yy[y[i]] = 1;
double layer3_error[MAX_FEATURE_DIMENSION] = {0};
for (int j = 1; j <= label_num; j++){
layer3_error[j] = a3[j] - yy[j];
}
double layer2_error[MAX_FEATURE_DIMENSION] = {0};
compute_layer_error(layer2_error, W2, label_num, hidden_layer_size, layer3_error, z2);
accumulate_gradient(grad2_sum, layer3_error, label_num, hidden_layer_size, a2);
accumulate_gradient(grad1_sum, layer2_error, hidden_layer_size, feature_number, X[i]);
}
for (int i = 0; i < hidden_layer_size; i++){
for (int j = 0; j <= feature_number; j++){
w1_grad[i][j] = grad1_sum[i][j] / sample_number;
}
}
for (int i = 0; i < label_num; i++){
for (int j = 0; j <= hidden_layer_size; j++){
w2_grad[i][j] = grad2_sum[i][j] / sample_number;
}
}
}
int main(){
double X[][MAX_FEATURE_DIMENSION] = {
{0, 0.084147, 0.090930},
{0, 0.090930, 0.065699},
{0, 2, 3}
};
int y[] = {1, 2, 2};
int hidden_layer_size = 4;
int label_num = 2;
int feature_number = 2;
int sample_number = 3;
double W1[][MAX_FEATURE_DIMENSION] = {
{0.084147, -0.027942, -0.099999},
{0.090930, 0.065699, -0.053657},
{0.014112, 0.098936, 0.042017},
{-0.075680, 0.041212, 0.099061},
};
double W2[][MAX_FEATURE_DIMENSION] = {
{0.084147, -0.075680, 0.065699, -0.054402, 0.042017},
{0.090930, -0.095892, 0.098936, -0.099999, 0.099061}
};
double a2[10][MAX_FEATURE_DIMENSION] = {0};
double a3[10][MAX_FEATURE_DIMENSION] = {0};
double w1_grad[10][MAX_FEATURE_DIMENSION] = {0};
double w2_grad[10][MAX_FEATURE_DIMENSION] = {0};
compute_gradient(X, y, feature_number, 3, W1,
hidden_layer_size, W2, label_num, w1_grad, w2_grad);
printf("w1_grad:\n");
for (int i = 0; i < hidden_layer_size; i++){
for (int j = 0; j <= feature_number; j++){
printf("%lf ", w1_grad[i][j]);
}
printf("\n");
}
printf("w2_grad:\n");
for (int i = 0; i < label_num; i++){
for (int j = 0; j <= hidden_layer_size; j++){
printf("%lf ", w2_grad[i][j]);
}
printf("\n");
}
return 0;
}
运行截图：
时间： 2024-11-05 14:42:53