deep learning(1)BP神经网络原理与练习
具体原理参考如下讲义：
1、神经网络
2、反向传导
看完材料1和2就可以梳理清楚bp神经网络的基本工作原理，下面通过一个C语言实现的程序来练习这个算法
//Backpropagation, 25x25x8 units, binary sigmoid function network
//Written by Thomas Riga, University of Genoa, Italy
//thomas@magister.magi.unige.it #include <iostream>
#include <fstream>
#include <conio.h>
#include <stdlib.h>
#include <math.h>
#include <ctype.h>
#include <stdio.h>
#include <float.h>
using namespace std; double **input,
*hidden,
**output,
**target,
*bias,
**weight_i_h,
**weight_h_o,
*errorsignal_hidden,
*errorsignal_output; int input_array_size,
hidden_array_size,
output_array_size,
max_patterns,
bias_array_size,
gaset = -,
number_of_input_patterns,
pattern,
file_loaded = ,
ytemp = ,
ztemp = ;
double learning_rate,
max_error_tollerance = 0.1;
char filename[];
#define IA 16807
#define IM 2147483647
#define AM (1.0 / IM)
#define IQ 127773
#define IR 2836
#define NTAB 32
#define NDIV (1+(IM-1) / NTAB)
#define EPS 1.2e-7
#define RNMX (1.0 - EPS)
int compare_output_to_target();
void load_data(char *arg);
void save_data(char *argres);
void forward_pass(int pattern);
void backward_pass(int pattern);
void custom();
void compute_output_pattern();
void get_file_name();
float bedlam(long *idum);
void learn();
void make();
void test();
void print_data();
void print_data_to_screen();
void print_data_to_file();
void output_to_screen();
int getnumber();
void change_learning_rate();
void initialize_net();
void clear_memory(); int main()
{
cout << "backpropagation network by Thomas Riga, University of Genoa, Italy" << endl;
for(;;) {
char choice;
cout << endl << "1. load data" << endl;
cout << "2. learn from data" << endl;
cout << "3. compute output pattern" << endl;
cout << "4. make new data file" << endl;
cout << "5. save data" << endl;
cout << "6. print data" << endl;
cout << "7. change learning rate" << endl;
cout << "8. exit" << endl << endl;
cout << "Enter your choice (1-8)";
do { choice = getch(); } while (choice != '' && choice != '' && choice != '' && choice != '' && choice != '' && choice != '' && choice != '' && choice != '');
switch(choice) {
case '':
{
if (file_loaded == ) clear_memory();
get_file_name();
file_loaded = ;
load_data(filename);
}
break;
case '': learn();
break;
case '': compute_output_pattern();
break;
case '': make();
break;
case '':
{
if (file_loaded == )
{
cout << endl
<< "there is no data loaded into memory"
<< endl;
break;
}
cout << endl << "enter a filename to save data to: ";
cin >> filename;
save_data(filename);
}
break;
case '': print_data();
break;
case '': change_learning_rate();
break;
case '': return ;
};
}
} void initialize_net()
{
int x;
input = new double * [number_of_input_patterns];
if(!input) { cout << endl << "memory problem!"; exit(); }
for(x=; x<number_of_input_patterns; x++)
{
input[x] = new double [input_array_size];
if(!input[x]) { cout << endl << "memory problem!"; exit(); }
}
hidden = new double [hidden_array_size];
if(!hidden) { cout << endl << "memory problem!"; exit(); }
output = new double * [number_of_input_patterns];
if(!output) { cout << endl << "memory problem!"; exit(); }
for(x=; x<number_of_input_patterns; x++)
{
output[x] = new double [output_array_size];
if(!output[x]) { cout << endl << "memory problem!"; exit(); }
}
target = new double * [number_of_input_patterns];
if(!target) { cout << endl << "memory problem!"; exit(); }
for(x=; x<number_of_input_patterns; x++)
{
target[x] = new double [output_array_size];
if(!target[x]) { cout << endl << "memory problem!"; exit(); }
}
bias = new double [bias_array_size];
if(!bias) { cout << endl << "memory problem!"; exit(); }
weight_i_h = new double * [input_array_size];
if(!weight_i_h) { cout << endl << "memory problem!"; exit(); }
for(x=; x<input_array_size; x++)
{
weight_i_h[x] = new double [hidden_array_size];
if(!weight_i_h[x]) { cout << endl << "memory problem!"; exit(); }
}
weight_h_o = new double * [hidden_array_size];
if(!weight_h_o) { cout << endl << "memory problem!"; exit(); }
for(x=; x<hidden_array_size; x++)
{
weight_h_o[x] = new double [output_array_size];
if(!weight_h_o[x]) { cout << endl << "memory problem!"; exit(); }
}
errorsignal_hidden = new double [hidden_array_size];
if(!errorsignal_hidden) { cout << endl << "memory problem!"; exit(); }
errorsignal_output = new double [output_array_size];
if(!errorsignal_output) { cout << endl << "memory problem!"; exit(); }
return;
} void learn()
{
if (file_loaded == )
{
cout << endl
<< "there is no data loaded into memory"
<< endl;
return;
}
cout << endl << "learning..." << endl << "press a key to return to menu" << endl;
register int y;
while(!kbhit()) {
for(y=; y<number_of_input_patterns; y++) {
forward_pass(y);
backward_pass(y);
}
if(compare_output_to_target()) {
cout << endl << "learning successful" << endl;
return;
} }
cout << endl << "learning not successful yet" << endl;
return;
} void load_data(char *arg) {
int x, y;
ifstream in(arg);
if(!in) { cout << endl << "failed to load data file" << endl; file_loaded = ; return; }
in >> input_array_size;
in >> hidden_array_size;
in >> output_array_size;
in >> learning_rate;
in >> number_of_input_patterns;
bias_array_size = hidden_array_size + output_array_size;
initialize_net();
for(x = ; x < bias_array_size; x++) in >> bias[x];
for(x=; x<input_array_size; x++) {
for(y=; y<hidden_array_size; y++) in >> weight_i_h[x][y];
}
for(x = ; x < hidden_array_size; x++) {
for(y=; y<output_array_size; y++) in >> weight_h_o[x][y];
}
for(x=; x < number_of_input_patterns; x++) {
for(y=; y<input_array_size; y++) in >> input[x][y];
}
for(x=; x < number_of_input_patterns; x++) {
for(y=; y<output_array_size; y++) in >> target[x][y];
}
in.close();
cout << endl << "data loaded" << endl;
return;
} void forward_pass(int pattern)
{
_control87(MCW_EM, MCW_EM);
register double temp=;
register int x,y; // INPUT -> HIDDEN
for(y=; y<hidden_array_size; y++) {
for(x=; x<input_array_size; x++) {
temp += (input[pattern][x] * weight_i_h[x][y]);
}
hidden[y] = (1.0 / (1.0 + exp(-1.0 * (temp + bias[y]))));
temp = ;
} // HIDDEN -> OUTPUT
for(y=; y<output_array_size; y++) {
for(x=; x<hidden_array_size; x++) {
temp += (hidden[x] * weight_h_o[x][y]);
}
output[pattern][y] = (1.0 / (1.0 + exp(-1.0 * (temp + bias[y + hidden_array_size]))));
temp = ;
}
return;
} void backward_pass(int pattern)
{
register int x, y;
register double temp = ; // COMPUTE ERRORSIGNAL FOR OUTPUT UNITS
for(x=; x<output_array_size; x++) {
errorsignal_output[x] = (target[pattern][x] - output[pattern][x]);
} // COMPUTE ERRORSIGNAL FOR HIDDEN UNITS
for(x=; x<hidden_array_size; x++) {
for(y=; y<output_array_size; y++) {
temp += (errorsignal_output[y] * weight_h_o[x][y]);
}
errorsignal_hidden[x] = hidden[x] * (-hidden[x]) * temp;
temp = 0.0;
} // ADJUST WEIGHTS OF CONNECTIONS FROM HIDDEN TO OUTPUT UNITS
double length = 0.0;
for (x=; x<hidden_array_size; x++) {
length += hidden[x]*hidden[x];
}
if (length<=0.1) length = 0.1;
for(x=; x<hidden_array_size; x++) {
for(y=; y<output_array_size; y++) {
weight_h_o[x][y] += (learning_rate * errorsignal_output[y] *
hidden[x]/length);
}
} // ADJUST BIASES OF HIDDEN UNITS
for(x=hidden_array_size; x<bias_array_size; x++) {
bias[x] += (learning_rate * errorsignal_output[x] / length);
} // ADJUST WEIGHTS OF CONNECTIONS FROM INPUT TO HIDDEN UNITS
length = 0.0;
for (x=; x<input_array_size; x++) {
length += input[pattern][x]*input[pattern][x];
}
if (length<=0.1) length = 0.1;
for(x=; x<input_array_size; x++) {
for(y=; y<hidden_array_size; y++) {
weight_i_h[x][y] += (learning_rate * errorsignal_hidden[y] *
input[pattern][x]/length);
}
} // ADJUST BIASES FOR OUTPUT UNITS
for(x=; x<hidden_array_size; x++) {
bias[x] += (learning_rate * errorsignal_hidden[x] / length);
}
return;
} int compare_output_to_target()
{
register int y,z;
register double temp, error = 0.0;
temp = target[ytemp][ztemp] - output[ytemp][ztemp];
if (temp < ) error -= temp;
else error += temp;
if(error > max_error_tollerance) return ;
error = 0.0;
for(y=; y < number_of_input_patterns; y++) {
for(z=; z < output_array_size; z++) {
temp = target[y][z] - output[y][z];
if (temp < ) error -= temp;
else error += temp;
if(error > max_error_tollerance) {
ytemp = y;
ztemp = z;
return ;
}
error = 0.0;
}
}
return ;
} void save_data(char *argres) {
int x, y;
ofstream out;
out.open(argres);
if(!out) { cout << endl << "failed to save file" << endl; return; }
out << input_array_size << endl;
out << hidden_array_size << endl;
out << output_array_size << endl;
out << learning_rate << endl;
out << number_of_input_patterns << endl << endl;
for(x=; x<bias_array_size; x++) out << bias[x] << ' ';
out << endl << endl;
for(x=; x<input_array_size; x++) {
for(y=; y<hidden_array_size; y++) out << weight_i_h[x][y] << ' ';
}
out << endl << endl;
for(x=; x<hidden_array_size; x++) {
for(y=; y<output_array_size; y++) out << weight_h_o[x][y] << ' ';
}
out << endl << endl;
for(x=; x<number_of_input_patterns; x++) {
for(y=; y<input_array_size; y++) out << input[x][y] << ' ';
out << endl;
}
out << endl;
for(x=; x<number_of_input_patterns; x++) {
for(y=; y<output_array_size; y++) out << target[x][y] << ' ';
out << endl;
}
out.close();
cout << endl << "data saved" << endl;
return;
} void make()
{
int x, y, z;
double inpx, bias_array_size, input_array_size, hidden_array_size, output_array_size;
char makefilename[];
cout << endl << "enter name of new data file: ";
cin >> makefilename;
ofstream out;
out.open(makefilename);
if(!out) { cout << endl << "failed to open file" << endl; return;}
cout << "how many input units? ";
cin >> input_array_size;
out << input_array_size << endl;
cout << "how many hidden units? ";
cin >> hidden_array_size;
out << hidden_array_size << endl;
cout << "how many output units? ";
cin >> output_array_size;
out << output_array_size << endl;
bias_array_size = hidden_array_size + output_array_size;
cout << endl << "Learning rate: ";
cin >> inpx;
out << inpx << endl;
cout << endl << "Number of input patterns: ";
cin >> z;
out << z << endl << endl;
for(x=; x<bias_array_size; x++) out << (1.0 - (2.0 * bedlam((long*)(gaset)))) << ' ';
out << endl << endl;
for(x=; x<input_array_size; x++) {
for(y=; y<hidden_array_size; y++) out << (1.0 - (2.0 * bedlam((long*)(gaset)))) << ' ';
}
out << endl << endl;
for(x=; x<hidden_array_size; x++) {
for(y=; y<output_array_size; y++) out << (1.0 - (2.0 * bedlam((long*)(gaset)))) << ' ';
}
out << endl << endl;
for(x=; x < z; x++) {
cout << endl << "input pattern " << (x + ) << endl;
for(y=; y<input_array_size; y++) {
cout << (y+) << ": ";
cin >> inpx;
out << inpx << ' ';
}
out << endl;
}
out << endl;
for(x=; x < z; x++) {
cout << endl << "target output pattern " << (x+) << endl;
for(y=; y<output_array_size; y++) {
cout << (y+) << ": ";
cin >> inpx;
out << inpx << ' ';
}
out << endl;
}
out.close();
cout << endl << "data saved, to work with this new data file you first have to load it" << endl;
return;
} float bedlam(long *idum)
{
int xj;
long xk;
static long iy=;
static long iv[NTAB];
float temp; if(*idum <= || !iy)
{
if(-(*idum) < )
{
*idum = + *idum;
}
else
{
*idum = -(*idum);
}
for(xj = NTAB+; xj >= ; xj--)
{
xk = (*idum) / IQ;
*idum = IA * (*idum - xk * IQ) - IR * xk;
if(*idum < )
{
*idum += IM;
}
if(xj < NTAB)
{
iv[xj] = *idum;
}
}
iy = iv[];
} xk = (*idum) / IQ;
*idum = IA * (*idum - xk * IQ) - IR * xk;
if(*idum < )
{
*idum += IM;
}
xj = iy / NDIV;
iy = iv[xj];
iv[xj] = *idum; if((temp=AM*iy) > RNMX)
{
return(RNMX);
}
else
{
return(temp);
}
} void test()
{
pattern = ;
while(pattern == ) {
cout << endl << endl << "There are " << number_of_input_patterns << " input patterns in the file," << endl << "enter a number within this range: ";
pattern = getnumber();
}
pattern--;
forward_pass(pattern);
output_to_screen();
return;
} void output_to_screen()
{
int x;
cout << endl << "Output pattern:" << endl;
for(x=; x<output_array_size; x++) {
cout << endl << (x+) << ": " << output[pattern][x] << " binary: ";
if(output[pattern][x] >= 0.9) cout << "";
else if(output[pattern][x]<=0.1) cout << "";
else cout << "intermediate value";
}
cout << endl;
return;
} int getnumber()
{
int a, b = ;
char c, d[];
while(b<) {
do { c = getch(); } while (c != '' && c != '' && c != '' && c != '' && c != '' && c != '' && c != '' && c != '' && c != '' && c != '' && toascii(c) != );
if(toascii(c)==) break;
if(toascii(c)==) return ;
d[b] = c;
cout << c;
b++;
}
d[b] = '\0';
a = atoi(d);
if(a < || a > number_of_input_patterns) a = ;
return a;
} void get_file_name()
{
cout << endl << "enter name of file to load: ";
cin >> filename;
return;
} void print_data()
{
char choice;
if (file_loaded == )
{
cout << endl
<< "there is no data loaded into memory"
<< endl;
return;
}
cout << endl << "1. print data to screen" << endl;
cout << "2. print data to file" << endl;
cout << "3. return to main menu" << endl << endl;
cout << "Enter your choice (1-3)" << endl;
do { choice = getch(); } while (choice != '' && choice != '' && choice != '');
switch(choice) {
case '': print_data_to_screen();
break;
case '': print_data_to_file();
break;
case '': return;
};
return;
} void print_data_to_screen() {
register int x, y;
cout << endl << endl << "DATA FILE: " << filename << endl;
cout << "learning rate: " << learning_rate << endl;
cout << "input units: " << input_array_size << endl;
cout << "hidden units: " << hidden_array_size << endl;
cout << "output units: " << output_array_size << endl;
cout << "number of input and target output patterns: " << number_of_input_patterns << endl << endl;
cout << "INPUT AND TARGET OUTPUT PATTERNS:";
for(x=; x<number_of_input_patterns; x++) {
cout << endl << "input pattern: " << (x+) << endl;
for(y=; y<input_array_size; y++) cout << input[x][y] << " ";
cout << endl << "target output pattern: " << (x+) << endl;
for(y=; y<output_array_size; y++) cout << target[x][y] << " ";
}
cout << endl << endl << "BIASES:" << endl;
for(x=; x<hidden_array_size; x++) {
cout << "bias of hidden unit " << (x+) << ": " << bias[x];
if(x<output_array_size) cout << " bias of output unit " << (x+) << ": " << bias[x+hidden_array_size];
cout << endl;
}
cout << endl << "WEIGHTS:" << endl;
for(x=; x<input_array_size; x++) {
for(y=; y<hidden_array_size; y++) cout << "i_h[" << x << "][" << y << "]: " << weight_i_h[x][y] << endl;
}
for(x=; x<hidden_array_size; x++) {
for(y=; y<output_array_size; y++) cout << "h_o[" << x << "][" << y << "]: " << weight_h_o[x][y] << endl;
}
return;
} void print_data_to_file()
{
char printfile[];
cout << endl << "enter name of file to print data to: ";
cin >> printfile;
ofstream out;
out.open(printfile);
if(!out) { cout << endl << "failed to open file"; return; }
register int x, y;
out << endl << endl << "DATA FILE: " << filename << endl;
out << "input units: " << input_array_size << endl;
out << "hidden units: " << hidden_array_size << endl;
out << "output units: " << output_array_size << endl;
out << "learning rate: " << learning_rate << endl;
out << "number of input and target output patterns: " << number_of_input_patterns << endl << endl;
out << "INPUT AND TARGET OUTPUT PATTERNS:";
for(x=; x<number_of_input_patterns; x++) {
out << endl << "input pattern: " << (x+) << endl;
for(y=; y<input_array_size; y++) out << input[x][y] << " ";
out << endl << "target output pattern: " << (x+) << endl;
for(y=; y<output_array_size; y++) out << target[x][y] << " ";
}
out << endl << endl << "BIASES:" << endl;
for(x=; x<hidden_array_size; x++) {
out << "bias of hidden unit " << (x+) << ": " << bias[x];
if(x<output_array_size) out << " bias of output unit " << (x+) << ": " << bias[x+hidden_array_size];
out << endl;
}
out << endl << "WEIGHTS:" << endl;
for(x=; x<input_array_size; x++) {
for(y=; y<hidden_array_size; y++) out << "i_h[" << x << "][" << y << "]: " << weight_i_h[x][y] << endl;
}
for(x=; x<hidden_array_size; x++) {
for(y=; y<output_array_size; y++) out << "h_o[" << x << "][" << y << "]: " << weight_h_o[x][y] << endl;
}
out.close();
cout << endl << "data has been printed to " << printfile << endl;
return;
} void change_learning_rate()
{
if (file_loaded == )
{
cout << endl
<< "there is no data loaded into memory"
<< endl;
return;
}
cout << endl << "actual learning rate: " << learning_rate << " new value: ";
cin >> learning_rate;
return;
} void compute_output_pattern()
{
if (file_loaded == )
{
cout << endl
<< "there is no data loaded into memory"
<< endl;
return;
}
char choice;
cout << endl << endl << "1. load trained input pattern into network" << endl;
cout << "2. load custom input pattern into network" << endl;
cout << "3. go back to main menu" << endl << endl;
cout << "Enter your choice (1-3)" << endl;
do { choice = getch(); } while (choice != '' && choice != '' && choice != '');
switch(choice) {
case '': test();
break;
case '': custom();
break;
case '': return;
};
} void custom()
{
_control87 (MCW_EM, MCW_EM);
char filename[];
register double temp=;
register int x,y;
double *custom_input = new double [input_array_size];
if(!custom_input)
{
cout << endl << "memory problem!";
return;
}
double *custom_output = new double [output_array_size];
if(!custom_output)
{
delete [] custom_input;
cout << endl << "memory problem!";
return;
}
cout << endl << endl << "enter file that contains test input pattern: ";
cin >> filename;
ifstream in(filename);
if(!in) { cout << endl << "failed to load data file" << endl; return; }
for(x = ; x < input_array_size; x++) {
in >> custom_input[x];
}
for(y=; y<hidden_array_size; y++) {
for(x=; x<input_array_size; x++) {
temp += (custom_input[x] * weight_i_h[x][y]);
}
hidden[y] = (1.0 / (1.0 + exp(-1.0 * (temp + bias[y]))));
temp = ;
}
for(y=; y<output_array_size; y++) {
for(x=; x<hidden_array_size; x++) {
temp += (hidden[x] * weight_h_o[x][y]);
}
custom_output[y] = (1.0 / (1.0 + exp(-1.0 * (temp + bias[y + hidden_array_size]))));
temp = ;
}
cout << endl << "Input pattern:" << endl;
for(x = ; x < input_array_size; x++) {
cout << "[" << (x + ) << ": " << custom_input[x] << "] ";
}
cout << endl << endl << "Output pattern:";
for(x=; x<output_array_size; x++) {
cout << endl << (x+) << ": " << custom_output[x] << " binary: ";
if(custom_output[x] >= 0.9) cout << "";
else if(custom_output[x]<=0.1) cout << "";
else cout << "intermediate value";
}
cout << endl;
delete [] custom_input;
delete [] custom_output;
return;
} void clear_memory()
{
int x;
for(x=; x<number_of_input_patterns; x++)
{
delete [] input[x];
}
delete [] input;
delete [] hidden;
for(x=; x<number_of_input_patterns; x++)
{
delete [] output[x];
}
delete [] output;
for(x=; x<number_of_input_patterns; x++)
{
delete [] target[x];
}
delete [] target;
delete [] bias;
for(x=; x<input_array_size; x++)
{
delete [] weight_i_h[x];
}
delete [] weight_i_h;
for(x=; x<hidden_array_size; x++)
{
delete [] weight_h_o[x];
}
delete [] weight_h_o;
delete [] errorsignal_hidden;
delete [] errorsignal_output;
file_loaded = ;
return;
}
初始化的神经网络的数据文件：
0.5 5.747781 -6.045236 1.206744 -41.245163 -0.249886 -0.35452 0.0718 -8.446443 9.25553 -6.50087 7.357942 7.777944 1.238442 15.957281 0.452741 -8.19198 9.140881 29.124746 9.806898 5.859479 -5.09182 -3.475694 -4.896269 6.320669 0.213897 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!explanation of datafile. Can be deleted. Not necessary for network to work!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! (number of input units)
(number of hidden units)
(number of output units)
0.5 (learning rate)
(number of input and target output patterns) (has to correspond to the amount of patterns at the end of the datafile)
5.747781 -6.045236 1.206744 -41.245163 -0.249886 -0.35452 0.0718 (biases of hidden and output units, first three are biases of the hidden units, last four are biases of the output units) -8.446443 9.25553 -6.50087 7.357942 7.777944 1.238442 (values of weights from input to hidden units) 15.957281 0.452741 -8.19198 9.140881 29.124746 9.806898 5.859479 -5.09182 -3.475694 -4.896269 6.320669 0.213897 (values of weights from hidden to output units) (input pattern #)
(input pattern #)
(input pattern #)
(input pattern #) (target output pattern #)
(target output pattern #)
(target output pattern #)
(target output pattern #) !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!! end of explanation of datafile. !!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
按照数据输入说明，可以再b.txt文件中保存输入数据[0, 1],对应的输入结果如下：
可以看到，输入[0,1]得到的结果为0110，与训练时候的结果一直。
最后，本代码没有深入测试过，同时也只有一个隐层，所以建议只用来配合梳理算法原理用。
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