这是本人在学习PCA降维的过程中，根据算法写成的C++代码。

PCA是模式识别中常见的特征降维的算法，其大体步骤可以分为以下几个部分：

（1）原始特征矩阵归一化处理

（2）求取归一化处理后特征矩阵的协方差矩阵

（3）计算协方差矩阵的特征值及其对应的特征向量

（4）按照特征值从大到小排列特征向量

（5）从大到小，挑选出前K个特征值对应的特征向量组成降维后的特征向量，即为所求。

注：在求取特征值和特征向量的过程中，借助了C++ Eigen库，需要自行安装和配置该库。

//PCA_Demension.h文件
#pragma once
#include<iostream>
#include<vector>
#include<map>
#include<Eigen/Dense>
using namespace Eigen;
using Eigen::MatrixXd;
using namespace std;
//pca降维代码的实现 2017.02.16 
//copyright: PH-SCUT
class PCA_Demension
{
public:PCA_Demension(void);~PCA_Demension(void);int covariance(vector<double> x, double x_mean, vector<double> y, double y_mean, double & result);int PCA_demension(vector<vector<double> > Feature_Data, int k, vector<vector<double> > & PCA_Features,vector<vector<double> > & Final_Data);
};

#include "PCA_Demension.h"PCA_Demension::PCA_Demension(void)
{
}PCA_Demension::~PCA_Demension(void)
{
}/*
函数名称：covariance
函数功能：协方差求取
输入：vector<double> x ---- 输入参量xdouble x_mean --- x的均值vector<double> y ---- 输入参量ydouble y_mean ---- y的均值
输出：double result --- 两列向量的协方差
*/
int PCA_Demension::covariance(vector<double> x, double x_mean, vector<double> y, double y_mean, double & result)
{double sum_temp = 0;for(size_t i = 0 ; i < x.size(); ++i){sum_temp = sum_temp + (x[i]-x_mean)*(y[i]-y_mean);	}result = sum_temp/(x.size() - 1);return 1;
}/*
函数名称：PCA_demension
函数功能：PCA降维
输入：vector<vector<double> > Feature_Data ---- 需要降维的数据，每一行是一个样本，每一列代表一个特征int k --- 降到K维
输出：vector<vector<double> > PCA_Features---中间变换特征矩阵vector<vector<double> >  Final_Data -----最终降维处理得到的答案
返回值: 1 --- 计算正确 ；0 --- 计算错误*/
int PCA_Demension::PCA_demension(vector<vector<double> > Feature_Data, int k, vector<vector<double> > & PCA_Features,vector<vector<double> > & Final_Data)
{//对每一列的数据求取平均值vector<double> Mean_values(Feature_Data[0].size(),0);//初始化for(size_t j = 0;j < Feature_Data[0].size(); ++j){double sum_temp = 0;for(size_t i = 0;i < Feature_Data.size(); ++i){sum_temp = sum_temp + Feature_Data[i][j];}Mean_values[j] = sum_temp/Feature_Data.size();}//对于所有样例都减去对应的平均值,去均值处理for(size_t j = 0;j<Feature_Data[0].size(); ++j){for(size_t i = 0;i<Feature_Data.size(); ++i){Feature_Data[i][j] = Feature_Data[i][j] - Mean_values[j];}}//求取特征协方差矩阵//在这之前，首先进行转置//实现转置功能vector<vector<double> > trans;for(size_t i=0;i<Feature_Data[0].size();i++){vector<double> temp;for(size_t j=0;j<Feature_Data.size();j++){temp.push_back(Feature_Data[j][i]);}trans.push_back(temp);temp.clear();}//实现求取协方差矩阵vector<vector<double> > covariance_Matrix;for(size_t i = 0;i<Feature_Data[0].size();++i){vector<double> temp;for(size_t j = 0;j<Feature_Data[0].size();++j){double result = 0;covariance(trans[i],Mean_values[i],trans[j],Mean_values[j],result);temp.push_back(result);}covariance_Matrix.push_back(temp);temp.clear();}//求协方差矩阵的特征值和特征向量/*vector<vector<double> > pca_result;double dbEps = 0.001;int nJt = 1000;JacbiCor(covariance_Matrix,k,dbEps,nJt,pca_result);*/MatrixXd covariance_Matrix_temp(covariance_Matrix.size(),covariance_Matrix.size());for(size_t i = 0 ; i< covariance_Matrix.size(); ++i){for(size_t j = 0 ; j< covariance_Matrix.size(); ++j){covariance_Matrix_temp(i,j) = covariance_Matrix[i][j];}}EigenSolver<MatrixXd> es(covariance_Matrix_temp);MatrixXd V = es.pseudoEigenvectors();cout<<"特征向量V ： "<< endl<< V<<endl;MatrixXd D = es.pseudoEigenvalueMatrix();cout<<"特征值矩阵D："<<endl<<D<<endl;//进行排序std::map<double,int> mapEigen;int D_row = D.rows();int V_row = V.rows();double * pdbEigenValues = new double[D_row];double * pdbVecs = new double[(D_row)*(D_row)]; for(size_t i =0; i < V_row; ++i){for(size_t j =0; j < V_row; ++j){pdbVecs[i*(V_row)+j] = V(j,i);}}double *pdbTmpVec = new double[(D_row)*(D_row)];for(size_t i = 0;i< D_row; ++i){pdbEigenValues[i] = D(i,i);mapEigen.insert(make_pair(pdbEigenValues[i],i));}std::map<double,int>::reverse_iterator iter = mapEigen.rbegin();for (int j = 0; iter != mapEigen.rend(),j < D_row; ++iter,++j){for (int i = 0; i < D_row; i ++){pdbTmpVec[j*D_row+i] = pdbVecs[i+ (iter->second)*D_row];}//特征值重新排列pdbEigenValues[j] = iter->first;}memcpy(pdbVecs,pdbTmpVec,sizeof(double)*(D_row)*(D_row));delete[] pdbTmpVec;//选择k个特征向量for(size_t i = 0 ;i< k ;++i){vector<double> temp;for(size_t j = 0; j< D_row; ++j){temp.push_back(pdbVecs[i*D_row+j]);//一行是一个向量}PCA_Features.push_back(temp);temp.clear();}delete[] pdbEigenValues;delete[] pdbVecs;//还有矩阵乘法//先对PCA_Features进行转置，看看情况vector<vector<double> > trans_fature;for(size_t i=0;i<PCA_Features[0].size();i++){vector<double> temp;for(size_t j=0;j<PCA_Features.size();j++){temp.push_back(PCA_Features[j][i]);}trans_fature.push_back(temp);temp.clear();}vector<vector<double> > Final_Data;for(size_t i = 0;i<Feature_Data.size();++i){vector<double> temp_v;for(size_t k = 0; k < trans_fature[0].size(); ++k){double temp_m = 0;for(size_t j = 0;j<Feature_Data[0].size(); ++j){temp_m = temp_m + Feature_Data[i][j]*trans_fature[j][k];}temp_v.push_back(temp_m);}Final_Data.push_back(temp_v);temp_v.clear();}return 1;
}