手写数字识别 神经网络 C++ 实现（三：ex4的实现）

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目录

 

实现基本架构类

Part 1: Loading and Visualizing Data 

Part 2: Loading Parameters

Part 3: Compute Cost (Feedforward) 

Part 4: Implement Regularization

Part 5: Sigmoid Gradient

 Part 6: Initializing Pameters

Part 7: Implement Backpropagation

Part 8: Training NN

完整代码：

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实现基本架构类

#include <core/core.hpp>    
#include <opencv2/opencv.hpp>
#include <iostream>  
#include <fstream>
#include <ostream>
#include <typeinfo>
#include <time.h>
using namespace std;
using namespace cv; 
class Nnetwork{
public:int visibleSize, hiddenSize, outputSize, layer_num;double lambda, cost, a;Mat data,//inputpre_data,pre_outp,outp,//output*b, *W, *bgrad, *Wgrad, *active_value, *test_Wgrad, *test_bgrad, *av;void initParam();Nnetwork();Nnetwork(int visiblesize, int hiddensize, int outpsize, int layernums, double lambda) :visibleSize(visiblesize),hiddenSize(hiddensize),outputSize(outpsize),layer_num(layernums),lambda(lambda){initParam();}Mat sigmoid(Mat matrix);double sigmoid(double num);Mat mat_exp(Mat r);Mat mat_log(Mat r);void forward_propagation();void showimage(Mat data, int pic_size, int num);void test_readdata();void test_readlabel();void test_load_Param();void test_nncost_1();void test_nncost_2();double test_nncost_3(int lambda, Mat *active_value, Mat *b, Mat *W);Mat sigmoidGradient(Mat inp);void writeMatToFile(cv::Mat& m, const char* filename);void computeNumericalGradient();Mat debugInitializeWeights(int fan_out, int fan_in);void checkNNGradients();void train();double predict();double pre_dict();void before_train();
};

Part 1: Loading and Visualizing Data 

Part 2: Loading Parameters

参见上一节：https://blog.csdn.net/Runner_of_nku/article/details/88815894

Part 3: Compute Cost (Feedforward) 

Part 4: Implement Regularization

这一步的前向传播是读取的上一节中的参数，我们需要实现的是代价函数，代码如下：

	void test_nncost_1(){delete[]active_value;active_value = new Mat[2];int data_size = outp.rows;active_value[0] = repeat(b[0], 1, data_size);active_value[1] = repeat(b[1], 1, data_size);active_value[0] = sigmoid(W[0]*data.t()+active_value[0]);active_value[1] = sigmoid(W[1]*active_value[0] + active_value[1]);Mat yk = Mat::zeros(10, data_size, CV_64FC1);for (int i = 0; i < data_size; i++)yk.at<double>(int(outp.at<double>(i, 0))-1,i) = 1;double J = sum((-1 * yk).mul(mat_log(active_value[1])) - (1 - yk).mul(mat_log(1 - active_value[1])))[0]/data_size;cout << "Cost at parameters (loaded from ex4weights)\n(this value should be about 0.287629)\n" << J<<endl;lambda=1;J += lambda / 2 / data_size * (sum(W[0].mul(W[0]))[0] + sum(W[1].mul(W[1]))[0]);cout << "Cost at parameters (loaded from ex4weights)\n(this value should be about 0.383770)\n" << J<<endl;cost = J;Mat delta3 = (active_value[1] - yk);Mat tem = (delta3.t()*W[1]).t();Mat delta2 = tem.mul(active_value[0]).mul(1 - active_value[0]);Wgrad[1] = delta3*active_value[0].t() / data_size + lambda*W[1] / data_size;Wgrad[0] = delta2*data / data_size + lambda*W[0] / data_size;bgrad[1] = Mat(delta3.rows, 1, CV_64FC1, Scalar::all(0));bgrad[0] = Mat(delta2.rows, 1, CV_64FC1, Scalar::all(0));reduce(delta3, bgrad[1], 1, 1);reduce(delta2, bgrad[0], 1, 1);}

Part 5: Sigmoid Gradient

这一节很简单，实现sigmoid函数的求导，我们在实际计算的时候可以直接写sigmoid(x)*(1-sigmoid(x))即可

 Part 6: Initializing Pameters

ex4中的随机数是直接给出了0.12，实际上这个0.12是怎么算出来的呢：

sqrt(6) / sqrt(hiddenSize + visibleSize + 1) ≈ 0.12

	void initParam(){a = 0.2;b = new Mat[layer_num];W = new Mat[layer_num];b[0] = Mat(hiddenSize, 1, CV_64FC1, Scalar(0));b[layer_num - 1] = Mat(outputSize, 1, CV_64FC1, Scalar(0));W[0] = Mat(hiddenSize, visibleSize, CV_64FC1);W[layer_num - 1] = Mat(outputSize, hiddenSize, CV_64FC1);for (int i = 1; i < layer_num - 1; i++){W[i] = Mat(hiddenSize, hiddenSize, CV_64FC1);b[i] = Mat(hiddenSize, 1, CV_64FC1, Scalar(0));}double r = sqrt(6) / sqrt(hiddenSize + visibleSize + 1);for (int i = 0; i < layer_num; i++){randu(W[i], Scalar::all

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