多层神经网络与C++实现
BP理论部分参考：http://blog.csdn.net/itplus/article/details/11022243
参考http://www.cnblogs.com/ronny/p/ann_02.html#!comments，结合BP算法的理论部分，可以真正理解了ANN。
代码部分我加了部分注释
#include<vector> using namespace std; //单个连接线 class NNconnection { public: //两个索引，一个与该结点相连（前一层）的前一层结点的索引， //一个对应的权值索引在整个单层网络中权值向量中的索引 unsigned weightIdx; unsigned neuralIdx; }; //单个神经元,包括一个输出和多个连接线 class NNneural { public: double output;//输出 vector<NNconnection> m_connection; }; //单层网络 class NNlayer { public: NNlayer *preLayer;//该层网络的前一层 NNlayer(){ preLayer = NULL; } vector<NNneural> m_neurals;//每层网络多个神经元 vector<double> m_weights;//权值向量 //加多少个神经元，及经前一层神经元的个数 void addNeurals(unsigned num, unsigned preNumNeurals); //反向传播 void backPropagate(vector<double>& ,vector<double>&,double); }; class NeuralNetwork { private: unsigned nLayer;//网络层数 vector<unsigned> nodes;//每层的结点数 vector<double> actualOutput;//每次迭代的输出结果 double etaLearningRate;//权值学习率 unsigned iterNum;//迭代次数 public: vector<NNlayer*>m_layers;//由多个单层网络组成 //创建网络，第二个参数为[48,25,30]，则表明该网络有三层，每层结点数分别为48，25，30 void create(unsigned num_layers, unsigned *ar_nodes); void initializeNetwork();//初始化网络，包括权值设置等 void forwardCalculate(vector<double> &invect, vector<double> &outvect);//向前计算 void backPropagate(vector<double>& tVect, vector<double>& oVect);//反向传播 void train(vector<vector<double>>& inputVec, vector<vector<double>>& outputVec);//训练 void classifier(vector<vector<double>>& inputVec, vector<vector<double>>& outputVec);//分类 }; void NeuralNetwork::initializeNetwork() { //初始化网络，创建各层和各层结点，初始化权值 // i为何如此定义？ for (vector<NNlayer*>::size_type i = 0; i != nLayer; i++) { NNlayer *ptrLayer = new NNlayer; if (i == 0) { ptrLayer->addNeurals(nodes[i], 0);//第一层之前的结点数为0 } else { ptrLayer->preLayer = m_layers[i - 1]; //每个神经元的初值包括与前一层神经元的连接索引和该层权重索引 ptrLayer->addNeurals(nodes[i], nodes[i - 1]); //连结权重个数 unsigned num_weights = nodes[i] * (nodes[i - 1] + 1);//+bias //初始化权重 for (vector<NNlayer*>::size_type k = 0; k != num_weights; k++) { ptrLayer->m_weights.push_back(0.05*rand() / RAND_MAX);//0~0.05 } } m_layers.push_back(ptrLayer); } } void NNlayer::addNeurals(unsigned num, unsigned preNumNeural) { for (vector<NNneural>::size_type i = 0; i != num; i++) { NNneural sneural; sneural.output = 0; for (vector<NNconnection>::size_type k = 0; k != preNumNeural; k++) { NNconnection sconnection; //给该神经元加上连接索引和权值索引 sconnection.weightIdx = i*(preNumNeural + 1) + k;//加1给偏置留一个索引位置 sconnection.neuralIdx = k; sneural.m_connection.push_back(sconnection); } m_neurals.push_back(sneural); } } void NeuralNetwork::forwardCalculate(vector<double> &invect, vector<double> &outvect) { actualOutput.clear(); vector<NNlayer*>::iterator layerIt = m_layers.begin(); while (layerIt != m_layers.end()) { if (layerIt == m_layers.begin()) { for (vector<NNneural>::size_type k = 0; k != (*layerIt)->m_neurals.size(); k++) { //对第一层的神经元来说，输出即为输入 (*layerIt)->m_neurals[k].output = invect[k]; } } else { vector<NNneural>::iterator neuralIt = (*layerIt)->m_neurals.begin(); int neuralIdx = 0; while (neuralIt != (*layerIt)->m_neurals.end()) { //每个神经元的连接线数 vector<NNconnection>::size_type num_connection = (*neuralIt).m_connection.size(); //偏置 double dsum = (*layerIt)->m_weights[num_connection*(neuralIdx + 1) - 1]; for (vector<NNconnection>::size_type i = 0; i != num_connection; i++) { //sum=sum+w*x; unsigned wgtIdx = (*neuralIt).m_connection[i].weightIdx; unsigned neuralIdx = (*neuralIt).m_connection[i].neuralIdx; dsum += (*layerIt)->preLayer->m_neurals[neuralIdx].output* (*layerIt)->m_weights[wgtIdx]; } neuralIt->output = SIGMOID(dsum); neuralIt++;//下一个神经元 neuralIdx++;//每个神经元的偏置不同 } } layerIt++;//下一层网络 } //将最后一层的结果保存至输出 NNlayer * lastLayer = m_layers[m_layers.size() - 1]; vector<NNneural>::iterator neuralIt = lastLayer->m_neurals.begin(); while (neuralIt != lastLayer->m_neurals.end()) { outvect.push_back(neuralIt->output); neuralIt++; } } void NeuralNetwork::backPropagate(vector<double>& tVect, vector<double>& oVect) { //首先取得最后一层迭代器 vector<NNlayer *>::iterator lit = m_layers.end() - 1; //用于保存最后一层所有结点误差 vector<double> dErrWrtDxLast((*lit)->m_neurals.size()); for (vector<NNneural>::size_type i = 0; i != (*lit)->m_neurals.size(); i++) { dErrWrtDxLast[i]=oVect[i] - tVect[i]; } //所有层的误差 vector<vector<double>> diffVect(nLayer); diffVect[nLayer - 1] = dErrWrtDxLast; //先将其他层误差设为0 for (unsigned int i = 0; i < nLayer - 1; i++) { //每层误差的个数要与神经元相等 diffVect[i].resize(m_layers[i]->m_neurals.size(), 0.0); } vector<NNlayer>::size_type i = m_layers.size() - 1; //对每一层调用BP算法，第一个参数为第i层输出误差 //第二个参数可作为下次调用的返回值 for (lit; lit>m_layers.begin(); lit--) { (*lit)->backPropagate(diffVect[i], diffVect[i - 1], etaLearningRate); i--; } diffVect.clear(); } void NNlayer::backPropagate(vector<double>& dErrWrtDxn, vector<double>& dErrWrtDxnm, double eta) { //三个参数分别代表第i层的误差，第i-1层的误差，学习速率 //计算每个神经元的误差 double output; vector<double> dErrWrtDyn(dErrWrtDxn.size());//每个神经元的残差 for (vector<NNneural>::size_type i = 0; i != m_neurals.size(); i++) { output = m_neurals[i].output; //计算第i层的残差，对于输出层，dErrWrtDxn表示误差，对于 //其他层，dErrWrtDxn表示w*（i+1层残差） dErrWrtDyn[i] = DSIGMOD(output)*dErrWrtDxn[i]; } //计算每个w的偏导数 unsigned ii(0); vector<NNneural>::iterator nit = m_neurals.begin(); vector<double> dErrWrtDwn(m_weights.size(), 0); while (nit != m_neurals.end()) { //对于每个神经元 for (vector<NNconnection>::size_type k = 0; k != (*nit).m_connection.size(); k++) { //对于每个权重连接 if (k == (*nit).m_connection.size() - 1) output = 1;//如果是偏置，则为1 else//与该权重相连的前一层神经元的输出 output = preLayer->m_neurals[(*nit).m_connection[k].neuralIdx].output; //计算该权重的偏导数值（随着迭代的进行，偏导也是逐渐累加的） dErrWrtDwn[((*nit).m_connection[k].weightIdx)] += output*dErrWrtDyn[ii]; } nit++; ii++; } //dErrWrtDxnm作为下一层的dErrWrtDxn，用于计算残差 unsigned j(0); nit = m_neurals.begin(); while (nit != m_neurals.end()) { for (vector<NNconnection>::size_type k = 0; k != (*nit).m_connection.size()-1; k++) { dErrWrtDxnm[(*nit).m_connection[k].neuralIdx] += dErrWrtDyn[j] * m_weights[(*nit).m_connection[k].weightIdx]; } j++; nit++; } for (vector<double>::size_type i = 0; i != m_weights.size(); i++) { m_weights[i] -= eta*dErrWrtDwn[i]; } }
