EM算法-最大期望算法(使用C++编写)

#include "em.h" #include "memory.h" #include "stdlib.h" #include "stdio.h" #include "math.h" #include "time.h" namespace ker { #define PI 3.1415926 //一个很小的数，用来解决协方差矩阵行列式为0以及高斯密度分布函数为0的问题 #define CONST_E 0.000000000001 cEm::cEm(int nVec, int nDim, int nPat) { _nVec = nVec; _nDim = nDim; _nPat = nPat; //_pplfZ[i][j]表示第i个向量属于第j类的概率,初始化为0 _pplfZ = new double *[_nVec]; for (int i = 0; i < _nVec; i++) { _pplfZ[i] = new double[_nPat]; memset(_pplfZ[i], 0, sizeof(double) * _nPat); } //_pplfU[i]表示第i类的均值向量，其初始化的值有可能导致陷入局部极值 //因此其初始化的值根据待分类数据来给出 _pplfU = new double *[_nPat]; for (int i = 0; i < _nPat; i++) { _pplfU[i] = new double[_nDim]; //for (int j = 0; j < _nDim; j++) _pplfU[i][j] = i * 2; } //_ppplfDelta[i]表示第i类的协方差矩阵,并把协方差矩阵初始化成单位阵 _ppplfDelta = new double **[_nPat]; for (int i = 0; i < _nPat; i++) { _ppplfDelta[i] = new double *[_nDim]; for (int j = 0; j < _nDim; j++) { _ppplfDelta[i][j] = new double[_nDim]; memset(_ppplfDelta[i][j], 0, sizeof(double) * _nDim); _ppplfDelta[i][j][j] = 1; } } //_plfPi[i]表示第i类的先验概率,初始化为1 / _nPat _plfPi = new double [_nPat]; for (int i = 0; i < _nPat; i++) _plfPi[i] = 1.0 / _nPat; } cEm::~cEm() { for (int i = 0; i < _nVec; i++) delete []_pplfZ[i]; delete []_pplfZ; for (int i = 0; i < _nPat; i++) delete[]_pplfU[i]; delete []_pplfU; for (int i = 0; i < _nPat; i++) { for (int j = 0; j < _nDim; j++) delete[]_ppplfDelta[i][j]; delete []_ppplfDelta[i]; } delete []_ppplfDelta; delete []_plfPi; } double **cEm::Inverse(double **pplfMatSrc) { //复制原矩阵 double **pplfMat = new double *[_nDim]; for (int i = 0; i < _nDim; i++) { pplfMat[i] = new double [_nDim]; memcpy(pplfMat[i], pplfMatSrc[i], sizeof(double) * _nDim); } //创建一个单位阵 double **pplfI = new double *[_nDim]; for (int i = 0; i < _nDim; i++) { pplfI[i] = new double [_nDim]; memset(pplfI[i], 0, sizeof(double) * _nDim); pplfI[i][i] = 1; } //Gaussian消元法求逆矩阵--正向消元 for (int i = 0; i < _nDim; i++) { double lfTmp = pplfMat[i][i]; for (int j = 0; j < _nDim; j++) { pplfMat[i][j] /= lfTmp; pplfI[i][j] /= lfTmp; } for (int j = i + 1; j < _nDim; j++) { double lfTmp = -pplfMat[j][i]; for (int k = 0; k < _nDim; k++) { pplfMat[j][k] += lfTmp * pplfMat[i][k]; pplfI[j][k] += lfTmp * pplfI[i][k]; } } } //Gaussian消元法求逆矩阵--逆向消元 for (int i = _nDim - 1; i >= 0; i--) for (int j = i - 1; j >= 0; j--) { double lfTmp = -pplfMat[j][i]; for (int k = 0; k < _nDim; k++) { pplfMat[j][k] += pplfMat[i][k] * lfTmp; pplfI[j][k] += pplfI[i][k] * lfTmp; } } //销毁临时空间 for (int i = 0; i < _nDim; i++) delete []pplfMat[i]; delete []pplfMat; return pplfI; } double cEm::Determinant(double **pplfMatSrc) { //复制原矩阵 double **pplfMat = new double *[_nDim]; for (int i = 0; i < _nDim; i++) { pplfMat[i] = new double [_nDim]; memcpy(pplfMat[i], pplfMatSrc[i], sizeof(double) * _nDim); } //Gaussian消元法--得到对角形式 for (int i = 0; i < _nDim; i++) { for (int j = i + 1; j < _nDim; j++) { double lfTmp = -pplfMat[j][i] / pplfMat[i][i]; for (int k = 0; k < _nDim; k++) pplfMat[j][k] += lfTmp * pplfMat[i][k]; } } //计算对角线乘积 double lfRs = 1; for (int i = 0; i < _nDim; i++) lfRs *= pplfMat[i][i]; //销毁临时空间 for (int i = 0; i < _nDim; i++) delete []pplfMat[i]; delete []pplfMat; return lfRs; } double cEm::Gaussian(double *plfVec, double *plfU, double **pplfDelta) { //整个函数是求多维高斯分布密度函数 double *plfTmp1 = new double[_nDim]; double *plfTmp2 = new double[_nDim]; for (int i = 0; i < _nDim; i++) plfTmp1[i] = plfVec[i] - plfU[i]; memset(plfTmp2, 0, sizeof(double) * _nDim); double **pplfInvDelta = Inverse(pplfDelta); for (int i = 0; i < _nDim; i++) for (int j = 0; j < _nDim; j++) plfTmp2[i] += plfTmp1[j] * pplfInvDelta[j][i]; double lfTmp1 = 0; for (int i = 0; i < _nDim; i++) lfTmp1 += plfTmp2[i] * plfTmp1[i]; lfTmp1 /= -2; lfTmp1 = exp(lfTmp1); double lfDelta = Determinant(pplfDelta); double lfTmp2 = 1 / sqrt (pow(2 * PI, _nDim) * lfDelta) * lfTmp1; for (int i = 0; i < _nDim; i++) delete []pplfInvDelta[i]; delete []pplfInvDelta; delete []plfTmp1; delete []plfTmp2; if (lfTmp2 < CONST_E) lfTmp2 = CONST_E; return lfTmp2; } void cEm::Expectation() { //E-Step _lfL = 0; for (int i = 0; i < _nVec; i++) { double lfSum = 0;//用于计算likelihood for (int j = 0; j < _nPat; j++) { double lfTmp = 0; for (int l = 0; l < _nPat; l++) { double lfG = Gaussian(_pplfVector[i], _pplfU[l], _ppplfDelta[l]); lfTmp += _plfPi[l] * lfG; } double lfG = Gaussian(_pplfVector[i], _pplfU[j], _ppplfDelta[j]); _pplfZ[i][j] = _plfPi[j] * lfG / lfTmp; lfSum += _plfPi[j] * lfG; } _lfL += log(lfSum); } } void cEm::Maximization() { //M-Step for (int j = 0; j < _nPat; j++) { double lfTmp1 = 0; for (int i = 0; i < _nVec; i++) lfTmp1 += _pplfZ[i][j]; //最大化步骤--求_pplfU[j] memset(_pplfU[j], 0, sizeof(double) * _nDim); for (int i = 0; i < _nVec; i++) for (int k = 0; k < _nDim; k++) _pplfU[j][k] += _pplfZ[i][j] * _pplfVector[i][k]; for (int k = 0; k < _nDim; k++) _pplfU[j][k] /= lfTmp1; //最大化步骤--求_ppplfDelta[j] for (int i = 0; i < _nDim; i++) memset(_ppplfDelta[j][i], 0, sizeof(double) * _nDim); for (int i = 0; i < _nVec; i++) { double *plfTmp = new double[_nDim]; for (int a = 0; a < _nDim; a++) plfTmp[a] = _pplfVector[i][a] - _pplfU[j][a]; //???????????????????????????????????????????????????????????? //这一步中只能忽略掉协方差，只考虑本身方差，为什么？跟公式不和! for (int a = 0; a < _nDim; a++)