training_nn.cpp

// Software: Training Artificial Neural Network for MNIST database
// Author: Hy Truong Son
// Major: BSc. Computer Science
// Class: 2013 - 2016
// Institution: Eotvos Lorand University
// Email: sonpascal93@gmail.com
// Website: http://people.inf.elte.hu/hytruongson/
// Copyright 2015 (c). All rights reserved.

#include<omp.h>
#include <iostream>
#include <fstream>
#include <cstring>
#include <string>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <vector>
#include <set>
#include <iterator>
#include <algorithm>

using namespace std;

// Training image file name
const string training_image_fn = "mnist/train-images.idx3-ubyte";

// Training label file name
const string training_label_fn = "mnist/train-labels.idx1-ubyte";

// Weights file name
const string model_fn = "model-neural-network.dat";

// Report file name
const string report_fn = "training-report.dat";

// Number of training samples
const int nTraining = 6000;

// Image size in MNIST database
const int width = 28;
const int height = 28;

// n1 = Number of input neurons
// n2 = Number of hidden neurons
// n3 = Number of output neurons
// epochs = Number of iterations for back-propagation algorithm
// learning_rate = Learing rate
// momentum = Momentum (heuristics to optimize back-propagation algorithm)
// epsilon = Epsilon, no more iterations if the learning error is smaller than epsilon

const int n1 = width * height; // = 784, without bias neuron 
const int n2 = 128; 
const int n3 = 10; // Ten classes: 0 - 9
const int epochs = 512;
const double learning_rate = 1e-3;
const double momentum = 0.9;
const double epsilon = 1e-3;

// From layer 1 to layer 2. Or: Input layer - Hidden layer
double *w1[n1 + 1], *delta1[n1 + 1], *out1;

// From layer 2 to layer 3. Or; Hidden layer - Output layer
double *w2[n2 + 1], *delta2[n2 + 1], *in2, *out2, *theta2;

// Layer 3 - Output layer
double *in3, *out3, *theta3;
double expected[n3 + 1];

// Image. In MNIST: 28x28 gray scale images.
int d[width + 1][height + 1];

// File stream to read data (image, label) and write down a report
ifstream image;
ifstream label;
ofstream report;

// +--------------------+
// | About the software |
// +--------------------+

void about() {
	// Details
	cout << "**************************************************" << endl;
	cout << "*** Training Neural Network for MNIST database ***" << endl;
	cout << "**************************************************" << endl;
	cout << endl;
	cout << "No. input neurons: " << n1 << endl;
	cout << "No. hidden neurons: " << n2 << endl;
	cout << "No. output neurons: " << n3 << endl;
	cout << endl;
	cout << "No. iterations: " << epochs << endl;
	cout << "Learning rate: " << learning_rate << endl;
	cout << "Momentum: " << momentum << endl;
	cout << "Epsilon: " << epsilon << endl;
	cout << endl;
	cout << "Training image data: " << training_image_fn << endl;
	cout << "Training label data: " << training_label_fn << endl;
	cout << "No. training sample: " << nTraining << endl << endl;
}

// +-----------------------------------+
// | Memory allocation for the network |
// +-----------------------------------+

void init_array() {
	// Layer 1 - Layer 2 = Input layer - Hidden layer
    for (int i = 1; i <= n1; ++i) {
        w1[i] = new double [n2 + 1];
        delta1[i] = new double [n2 + 1];
    }
    
    out1 = new double [n1 + 1];

	// Layer 2 - Layer 3 = Hidden layer - Output layer
    for (int i = 1; i <= n2; ++i) {
        w2[i] = new double [n3 + 1];
        delta2[i] = new double [n3 + 1];
    }
    
    in2 = new double [n2 + 1];
    out2 = new double [n2 + 1];
    theta2 = new double [n2 + 1];

	// Layer 3 - Output layer
    in3 = new double [n3 + 1];
    out3 = new double [n3 + 1];
    theta3 = new double [n3 + 1];
    
    // Initialization for weights from Input layer to Hidden layer
    for (int i = 1; i <= n1; ++i) {
        for (int j = 1; j <= n2; ++j) {
            int sign = rand() % 2;

            // Another strategy to randomize the weights - quite good 
            // w1[i][j] = (double)(rand() % 10 + 1) / (10 * n2);
            
            w1[i][j] = (double)(rand() % 6) / 10.0;
            if (sign == 1) {
				w1[i][j] = - w1[i][j];
			}
        }
	}
	
	// Initialization for weights from Hidden layer to Output layer
    for (int i = 1; i <= n2; ++i) {
        for (int j = 1; j <= n3; ++j) {
            int sign = rand() % 2;
			
			// Another strategy to randomize the weights - quite good 
            // w2[i][j] = (double)(rand() % 6) / 10.0;

            w2[i][j] = (double)(rand() % 10 + 1) / (10.0 * n3);
            if (sign == 1) {
				w2[i][j] = - w2[i][j];
			}
        }
	}
}

// +------------------+
// | Sigmoid function |
// +------------------+

double sigmoid(double x) {
    return 1.0 / (1.0 + exp(-x));
}

// +------------------------------+
// | Forward process - Perceptron |
// +------------------------------+

void perceptron() {
    for (int i = 1; i <= n2; ++i) {
		in2[i] = 0.0;
	}

    for (int i = 1; i <= n3; ++i) {
		in3[i] = 0.0;
	}

    for (int i = 1; i <= n1; ++i) {
        for (int j = 1; j <= n2; ++j) {
            in2[j] += out1[i] * w1[i][j];
		}
	}

    for (int i = 1; i <= n2; ++i) {
		out2[i] = sigmoid(in2[i]);
	}

    for (int i = 1; i <= n2; ++i) {
        for (int j = 1; j <= n3; ++j) {
            in3[j] += out2[i] * w2[i][j];
		}
	}

    for (int i = 1; i <= n3; ++i) {
		out3[i] = sigmoid(in3[i]);
	}
}

// +---------------+
// | Norm L2 error |
// +---------------+

double square_error(){
    double res = 0.0;
    for (int i = 1; i <= n3; ++i) {
        res += (out3[i] - expected[i]) * (out3[i] - expected[i]);
	}
    res *= 0.5;
    return res;
}

// +----------------------------+
// | Back Propagation Algorithm |
// +----------------------------+

void back_propagation() {
    double sum;

    for (int i = 1; i <= n3; ++i) {
        theta3[i] = out3[i] * (1 - out3[i]) * (expected[i] - out3[i]);
	}

    for (int i = 1; i <= n2; ++i) {
        sum = 0.0;
        for (int j = 1; j <= n3; ++j) {
            sum += w2[i][j] * theta3[j];
		}
        theta2[i] = out2[i] * (1 - out2[i]) * sum;
    }

    for (int i = 1; i <= n2; ++i) {
        for (int j = 1; j <= n3; ++j) {
            delta2[i][j] = (learning_rate * theta3[j] * out2[i]) + (momentum * delta2[i][j]);
            w2[i][j] += delta2[i][j];
        }
	}

    for (int i = 1; i <= n1; ++i) {
        for (int j = 1 ; j <= n2 ; j++ ) {
            delta1[i][j] = (learning_rate * theta2[j] * out1[i]) + (momentum * delta1[i][j]);
            w1[i][j] += delta1[i][j];
        }
	}
}

// +-------------------------------------------------+
// | Learning process: Perceptron - Back propagation |
// +-------------------------------------------------+

int learning_process() {
    for (int i = 1; i <= n1; ++i) {
        for (int j = 1; j <= n2; ++j) {
			delta1[i][j] = 0.0;
		}
	}

    for (int i = 1; i <= n2; ++i) {
        for (int j = 1; j <= n3; ++j) {
			delta2[i][j] = 0.0;
		}
	}

    for (int i = 1; i <= epochs; ++i) {
        perceptron();
        back_propagation();
        if (square_error() < epsilon) {
			return i;
		}
    }
    return epochs;
}

// +--------------------------------------------------------------+
// | Reading input - gray scale image and the corresponding label |
// +--------------------------------------------------------------+

void input() {
	// Reading image
    char number;
    for (int j = 1; j <= height; ++j) {
        for (int i = 1; i <= width; ++i) {
            image.read(&number, sizeof(char));
            if (number == 0) {
				d[i][j] = 0; 
			} else {
				d[i][j] = 1;
			}
        }
	}
	
	// cout << "Image:" << endl;
	for (int j = 1; j <= height; ++j) {
		for (int i = 1; i <= width; ++i) {
			// cout << d[i][j];
		}
		// cout << endl;
	}

    for (int j = 1; j <= height; ++j) {
        for (int i = 1; i <= width; ++i) {
            int pos = i + (j - 1) * width;
            out1[pos] = d[i][j];
        }
	}

	// Reading label
    label.read(&number, sizeof(char));
    for (int i = 1; i <= n3; ++i) {
		expected[i] = 0.0;
	}
    expected[number + 1] = 1.0;
    
    // cout << "Label: " << (int)(number) << endl;
}

// +------------------------+
// | Saving weights to file |
// +------------------------+

void write_matrix(string file_name) {
    ofstream file(file_name.c_str(), ios::out);
	
	// Input layer - Hidden layer
    for (int i = 1; i <= n1; ++i) {
        for (int j = 1; j <= n2; ++j) {
			file << w1[i][j] << " ";
		}
		file << endl;
    }
	
	// Hidden layer - Output layer
    for (int i = 1; i <= n2; ++i) {
        for (int j = 1; j <= n3; ++j) {
			file << w2[i][j] << " ";
		}
        file << endl;
    }
	
	file.close();
}

// +--------------+
// | Main Program |
// +--------------+

int main(int argc, char *argv[]) {
	about();
	
    report.open(report_fn.c_str(), ios::out);
    image.open(training_image_fn.c_str(), ios::in | ios::binary); // Binary image file
    label.open(training_label_fn.c_str(), ios::in | ios::binary ); // Binary label file

	// Reading file headers
    char number;
    for (int i = 1; i <= 16; ++i) {
        image.read(&number, sizeof(char));
	}
    for (int i = 1; i <= 8; ++i) {
        label.read(&number, sizeof(char));
	}
		
	// Neural Network Initialization
    init_array();

	double t1 = omp_get_wtime();
    
    for (int sample = 1; sample <= nTraining; ++sample) {
        // cout << "Sample " << sample << endl;
        
        // Getting (image, label)
        input();
		
		// Learning process: Perceptron (Forward procedure) - Back propagation
        int nIterations = learning_process();

		// Write down the squared error
		//cout << "No. iterations: " << nIterations << endl;
       //printf("Error: %0.6lf\n\n", square_error());
        report << "Sample " << sample << ": No. iterations = " << nIterations << ", Error = " << square_error() << endl;
		
		// Save the current network (weights)
		if (sample % 100 == 0) {
			cout << "Saving the network to " << model_fn << " file." << endl;
			write_matrix(model_fn);
		}
    }
	double t2 = omp_get_wtime();

	cout<<(t2-t1);
	
	// Save the final network
    write_matrix(model_fn);

    report.close();
    image.close();
    label.close();
    
    return 0;
}