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];
    }
}