一个类精通B-P网络的精髓

基于机器学习库的神经网络代码已经非常精简了，对于用户来说都是黑盒子，其内部到底怎么运作的呢？原理虽然简单，但真正要操刀书写，估计一时半会也不好弄，幸好大牛们开源了、只需要一个类就能明明白白！！！

backprop.h

////////////////////////////////////////////////Fully connected multilayered feed////forwardartificial neural network using////Backpropogationalgorithm for training.////////////////////////////////////////////////// 基于反向传播算法的全连接多层前向人工神经网络#ifndef backprop_h#define backprop_h#include <assert.h>#include <iostream>#include <stdio.h>#include <math.h>using namespace std;//B-P网络class CBackProp{//output of each neurondouble **out;//delta error value for each neurondouble **delta;//vector of weights for each neurondouble ***weight;//no of layers in net//including input layerint numl;//vector of numl elements for size //of each layerint *lsize;//learning rate //学习率double beta;//momentum parameter //动量参数double alpha;//storage for weight-change made ////in previous epochdouble ***prevDwt;//squashing function //压缩函数double sigmoid(double in);public:~CBackProp();//initializes and allocates memoryCBackProp(int nl,int *sz,double b,double a);//backpropogates error for one set of input //反向传播void bpgt(double *in,double *tgt);//feed forwards activations for one set of inputs //前向激活void ffwd(double *in);//returns mean square error of the net //均方误差double mse(double *tgt) const;//returns i'th output of the net //输出double Out(int i) const;};#endif

backprop.cpp

#include "backprop.h"#include <time.h>#include <stdlib.h>//initializes and allocates memory on heapCBackProp::CBackProp(int nl,int *sz,double b,double a): beta(b), alpha(a){int i=0;//set no of layers and their sizes //网络层数和节点数numl = nl;lsize = new int[numl];for(int i=0;i<numl;i++){lsize[i] = sz[i];}//allocate memory for output of each neuronout = new double*[numl];for( i=0;i<numl;i++){out[i] = new double[lsize[i]];}//allocate memory for deltadelta = new double*[numl];for(i=1;i<numl;i++){delta[i] = new double[lsize[i]];}//allocate memory for weightsweight = new double**[numl];for(i=1;i<numl;i++){weight[i] = new double*[lsize[i]];}for(i=1;i<numl;i++){for(int j=0;j<lsize[i];j++){weight[i][j] = new double[lsize[i-1]+1];}}//allocate memory for previous weightsprevDwt = new double**[numl];for(i=1;i<numl;i++){prevDwt[i] = new double*[lsize[i]];}for(i=1;i<numl;i++){for(int j=0;j<lsize[i];j++){prevDwt[i][j] = new double[lsize[i-1]+1];}}//seed and assign random weightssrand((unsigned)(time(NULL)));for(i=1;i<numl;i++){for(int j=0;j<lsize[i];j++){for(int k=0;k<lsize[i-1]+1;k++){weight[i][j][k] = (double)(rand())/(RAND_MAX/2) - 1;//32767}}}//initialize previous weights to 0 for first iterationfor(i=1;i<numl;i++){for(int j=0;j<lsize[i];j++){for(int k=0;k<lsize[i-1]+1;k++){prevDwt[i][j][k] = (double)0.0;}}}// Note that the following variables are unused,//// delta[0]// weight[0]// prevDwt[0]//  I did this intentionaly to maintains consistancy in numbering the layers.//  Since for a net having n layers, input layer is refered to as 0th layer,//  first hidden layer as 1st layer and the nth layer as output layer. And //  first (0th) layer just stores the inputs hence there is no delta or weigth//  values corresponding to it.}CBackProp::~CBackProp(){int i=0;//free outfor(i=0;i<numl;i++){delete[] out[i];}delete[] out;//free deltafor(i=1;i<numl;i++){delete[] delta[i];}delete[] delta;//free weightfor(i=1;i<numl;i++){for(int j=0;j<lsize[i];j++){delete[] weight[i][j];}}for(i=1;i<numl;i++){delete[] weight[i];}delete[] weight;//free prevDwtfor(i=1;i<numl;i++){for(int j=0;j<lsize[i];j++){delete[] prevDwt[i][j];}}for(i=1;i<numl;i++){delete[] prevDwt[i];}delete[] prevDwt;//free layer infodelete[] lsize;}//sigmoid function //激活函数double CBackProp::sigmoid(double in){return (double)(1/(1+exp(-in)));}//mean square error //均方差double CBackProp::mse(double *tgt) const{double mse=0;for(int i=0;i<lsize[numl-1];i++){mse += (tgt[i]-out[numl-1][i])*(tgt[i]-out[numl-1][i]);}return mse/2;}//returns i'th output of the net //输出网络结果double CBackProp::Out(int i) const{return out[numl-1][i];}// feed forward one set of input //对输入进行前向传播计算void CBackProp::ffwd(double *in){double sum;int i=0;//assign content to input layerfor(i=0;i<lsize[0];i++){out[0][i]=in[i];  // output_from_neuron(i,j) Jth neuron in Ith Layer}//assign output(activation) value //to each neuron usng sigmoid funcfor(i=1;i<numl;i++){// For each layerfor(int j=0;j<lsize[i];j++){// For each neuron in current layersum = 0.0;for(int k=0;k<lsize[i-1];k++){// For input from each neuron in preceeding layersum += out[i-1][k]*weight[i][j][k];// Apply weight to inputs and add to sum}sum += weight[i][j][lsize[i-1]];// Apply biasout[i][j] = sigmoid(sum);// Apply sigmoid function}}}//backpropogate errors from output//layer uptill the first hidden layer //反向传播误差直到第一个隐含层void CBackProp::bpgt(double *in,double *tgt){double sum;int i=0;//update output values for each neuronffwd(in);//find delta for output layerfor(i=0;i<lsize[numl-1];i++){delta[numl-1][i] = out[numl-1][i]*(1-out[numl-1][i])*(tgt[i]-out[numl-1][i]);}//find delta for hidden layersfor(i=numl-2;i>0;i--){for(int j=0;j<lsize[i];j++){sum = 0.0;for(int k=0;k<lsize[i+1];k++){sum += delta[i+1][k]*weight[i+1][k][j];}delta[i][j] = out[i][j]*(1-out[i][j])*sum;}}//apply momentum ( does nothing if alpha=0 )for(i=1;i<numl;i++){for(int j=0;j<lsize[i];j++){for(int k=0;k<lsize[i-1];k++){weight[i][j][k] += alpha*prevDwt[i][j][k];}weight[i][j][lsize[i-1]] += alpha*prevDwt[i][j][lsize[i-1]];}}//adjust weights usng steepest descentfor(i=1;i<numl;i++){for(int j=0;j<lsize[i];j++){for(int k=0;k<lsize[i-1];k++){prevDwt[i][j][k] = beta*delta[i][j]*out[i-1][k];weight[i][j][k] += prevDwt[i][j][k];}prevDwt[i][j][lsize[i-1]] = beta*delta[i][j];weight[i][j][lsize[i-1]] += prevDwt[i][j][lsize[i-1]];}}}

main.cpp

#include "BackProp.h"// NeuralNet.cpp : Defines the entry point for the console application.////异或运算int main(int argc, char* argv[]){// prepare XOR traing data //训练数据，最后一列为结果double data[][4] = {0,0,0,0,0,0,1,1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,1,1,1,1 };// prepare test data //测试数据double testData[][3]={0,  0,  0, //0                0,  0,  1, //1                0,  1,  0, //1                0,  1,  1, //0                1,  0,  0, //1                1,  0,  1, //0                1,  1,  0, //0                1,  1,  1 };//1// defining a net with 4 layers having 3,3,3, and 1 neuron respectively,// the first layer is input layer i.e. simply holder for the input parameters// and has to be the same size as the no of input parameters, in out example 3int numLayers = 4, lSz[4] = {3,3,2,1}; //网络层数、每层节点个数// Learing rate - beta //学习率// momentum - alpha //动量// Threshhold - thresh (value of target mse, training stops once it is achieved) //精度阈值double beta = 0.3, alpha = 0.1, Thresh =  0.00001;// maximum no of iterations during traininglong num_iter = 2000000; //最大轮数// Creating the netCBackProp *bp = new CBackProp(numLayers, lSz, beta, alpha);long i=0;cout<< endl <<  "Now training the network...." << endl;for (i=0; i<num_iter; i++)//训练轮数{bp->bpgt(data[i%8], &data[i%8][3]);//反向传播调整网络权重if( bp->mse(&data[i%8][3]) < Thresh )//达到精度，停止训练{cout << endl << "Network Trained. Threshold value achieved in " << i << " iterations." << endl;cout << "MSE:  " << bp->mse(&data[i%8][3])  <<  endl <<  endl;break;}if ( i%(num_iter/10) == 0 )//每10轮输出训练结果{cout<<  endl <<  "MSE:  " << bp->mse(&data[i%8][3]) << "... Training..." << endl;}}if ( i == num_iter ){cout << endl << i << " iterations completed..." << "MSE: " << bp->mse(&data[(i-1)%8][3]) << endl;}cout<< "Now using the trained network to make predctions on test data...." << endl << endl;for ( i = 0 ; i < 8 ; i++ ){bp->ffwd(testData[i]);//对测试数据进行预测cout << testData[i][0]<< "  " << testData[i][1]<< "  "  << testData[i][2]<< "  " << bp->Out(0) << endl;}return 0;}

结果很好：

back propagation算法

https://www.zhihu.com/question/27239198#answer-31377317