這是本人在學習PCA降維的過程中，根據算法寫成的C++代碼。

PCA是模式識別中常見的特征降維的算法，其大體步驟可以分為以下幾個部分：

（1）原始特征矩陣歸一化處理

（2）求取歸一化處理后特征矩陣的協方差矩陣

（3）計算協方差矩陣的特征值及其對應的特征向量

（4）按照特征值從大到小排列特征向量

（5）從大到小，挑選出前K個特征值對應的特征向量組成降維后的特征向量，即為所求。

注：在求取特征值和特征向量的過程中，借助了C++ Eigen庫，需要自行安裝和配置該庫。

//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降維代碼的實現 2017.02.16 //copyright: PH-SCUTclass 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){}/*函數名稱：covariance函數功能：協方差求取輸入：vector<double> x ---- 輸入參量x      double x_mean --- x的均值	  vector<double> y ---- 輸入參量y	  double y_mean ---- y的均值輸出：double result --- 兩列向量的協方差*/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;}/*函數名稱：PCA_demension函數功能：PCA降維輸入：vector<vector<double> > Feature_Data ---- 需要降維的數據，每一行是一個樣本，每一列代表一個特征      int k --- 降到K維輸出：vector<vector<double> > PCA_Features---中間變換特征矩陣          vector<vector<double> >  Final_Data -----最終降維處理得到的答案返回值: 1 --- 計算正確 ；0 --- 計算錯誤*/int PCA_Demension::PCA_demension(vector<vector<double> > Feature_Data, int k, vector<vector<double> > & PCA_Features,vector<vector<double> > & Final_Data){	//對每一列的數據求取平均值	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();	}		//對于所有樣例都減去對應的平均值,去均值處理	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];		}	}		//求取特征協方差矩陣	//在這之前，首先進行轉置	//實現轉置功能	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();	}	//實現求取協方差矩陣	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();	}		//求協方差矩陣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<<"特征值矩陣D："<<endl<<D<<endl;	//進行排序	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;	//選擇k個特征向量	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]);//一行是一個向量		}		PCA_Features.push_back(temp);		temp.clear();	}	delete[] pdbEigenValues;	delete[] pdbVecs;	//還有矩陣乘法	//先對PCA_Features進行轉置，看看情況	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;}