有人可以向我解释如何在 openCv c++ 中使用 SVM 和回归吗？回归应该返回一个值，这个值可以是图像中的一个位置（坐标 x 和 y）？还是一个数字？
我必须在视频分析中使用它。我有三个点，我知道整个视频的轨迹。我想用其中两个的轨迹来推断第三个的轨迹。所以我想用这些轨迹训练一个 SVM。
我正在考虑像这样组织我的训练数据和标签：
这是正确的方法吗？或者我应该这样组织它：
SVM 可用于回归：请参见此处http://alex.smola.org/papers/2003/SmoSch03b.pdf 但可能对于您的问题将更适合多元 RVM，请参见此处（使用 C++ 源）：http:// mi.eng.cam.ac.uk/~at315/MVRVM.htm
这是我的这段代码的opencv版本：
#include<iostream>
#include<fstream>
#include<cstdlib>
#include<windows.h>
#include<string>
#include<vector>
#include<opencv2/opencv.hpp>
using namespace std;
using namespace cv;
#define COUT_VAR(x) cout << #x"=" << x << endl;
#define SHOW_IMG(x) namedWindow(#x);imshow(#x,x);waitKey(20);
//calculates the conolution of two ploynoimals
// n - size of polynomial x
// m - size of polynomial y
// z - resultant polynomial after the convolution
void conv(int n,int m,double* x,double* y,double* z)
{
int i,j;
for(i=0; i<(n+m-1); i++)
{
z[i]=0.0;
for(j=0; j<n; j++)
{
if(((i-j)>=0)&& ((i-j)<m))
{
z[i]+=x[j]*y[i-j];
}
}
}
}
//calculates poly noimal coeefeicents from a number of roots
//input
//n - number of roots
//x - array of roots
//ouput
//y - array of polynomial coefficnets
void poly(int n,double* x,double* y)
{
int i,j;
for(j=0; j<=n; j++)
{
y[j]=0.0;
}
y[0]=1;
double temp[20];
for(j=0; j<n; j++)
{
for(i=0; i<=(j); i++)
{
temp[i+1]=y[i+1]-x[j]*y[i];
}
for(i=0; i<=(j); i++)
{
y[i+1]=temp[i+1];
}
}
}
//find the roots of a polynomial
int Roots(int n,double* cof,double*roots)
{
bool fnzf=false;
int k=0,i;
double acof[100];
for(i=0; i<n; i++)
{
if(!fnzf)
{
if(fabs(cof[i])>10e-6)
{
fnzf=true;
acof[k]=cof[i];
k++;
}
}
else
{
acof[k]=cof[i];
k++;
}
}
if(k==0)
{
return 0;
}
Mat a(k,1,CV_64FC1);
for(i=0; i<k; i++)
{
a.at<double>(i)=acof[i];
}
Mat r;
cv::solvePoly(a,r);
Mat ch[2];
cv::split(r,ch);
Mat b=ch[0].clone();
for(i=0; i<b.rows; i++)
{
roots[i]=b.at<double>(i);
}
return b.rows;
}
//this function sloves a polynomial equation of a single hyperparameter
void SolveForAlpha(int n,Mat& q, Mat& s,Mat& Q,Mat S,double old_alpha,double& newAlpha,double& l_inc)
{
double ALPHA_MAX=1e12;
double C[500], P[500], PP[500], SS[500], CC[500];
int i,k,j;
for(i=0; i<n; i++)
{
C[i]=0.0;
}
for(i=0; i<(2*n-1); i++)
{
CC[i]=0.0;
}
for(i=0; i<n; i++)
{
k=0;
for(j=0; j<n; j++)
{
if(i==j)
{
continue;
}
SS[k]=-s.at<double>(j);
k++;
}
poly(n-1,SS,P);
conv(n,n,P,P,PP);
for(j=0; j<n; j++)
{
C[j]=C[j]+P[j];
}
for(j=0; j<(2*n-1); j++)
{
CC[j]=CC[j]+ q.at<double>(i)*q.at<double>(i)*PP[j];
}
}
for(i=0; i<n; i++)
{
SS[i]=-s.at<double>(i);
}
poly(n,SS,P);
conv(n+1,n+1,P,P,PP);
for(i=0; i<(2*n+1); i++)
{
PP[i]=n*PP[i];
}
double CC0[500];
conv(n+1,n,P,C,CC0);
double CCC[500];
CCC[0]=CC0[0];
for(i=1; i<(2*n); i++)
{
CCC[i]=CC[i-1]+CC0[i];
}
CCC[2*n]=0;
bool fnonzero=false;
double aa[1000];
k=0;
for(i=0; i<(2*n+1); i++)
{
aa[i]=PP[i]-CCC[i];
}
double roots[100];
int nroots=Roots(2*n+1,aa,roots);
roots[nroots]=ALPHA_MAX;
nroots++;
double L[100];
double alphas[100];
for(i=0; i<100; i++)
{
L[i]=0.0;
}
k=0;
for( i=0; i<nroots; i++)
{
if(roots[i]<=0)
{
continue;
}
double new_alpha=roots[i];
if((old_alpha>=(ALPHA_MAX-1))&& (new_alpha<ALPHA_MAX))
{
alphas[k]=new_alpha;
for(j=0; j<n; j++)
{
L[k]=L[k]+ log(new_alpha/(new_alpha+s.at<double>(j)))+((q.at<double>(j)*q.at<double>(j)/(new_alpha+s.at<double>(j))));
}
}
else if((old_alpha<ALPHA_MAX)&& (new_alpha>=(ALPHA_MAX-1)))
{
alphas[k]=new_alpha;
for(j=0; j<n; j++)
{
L[k]=L[k]- log(old_alpha/(old_alpha+s.at<double>(j)))-((q.at<double>(j)*q.at<double>(j)/(old_alpha+s.at<double>(j))));
}
}
else if((old_alpha<ALPHA_MAX)&&(new_alpha<ALPHA_MAX))
{
alphas[k]=new_alpha;
double ad=(1/new_alpha)-(1/old_alpha);
for (j=0; j<n; j++)
{
L[k]=L[k]+ log(new_alpha/(new_alpha+s.at<double>(j)))+((q.at<double>(j)*q.at<double>(j)/(new_alpha+s.at<double>(j)))) -log(old_alpha/(old_alpha+s.at<double>(j)))-((q.at<double>(j)*q.at<double>(j)/(old_alpha+s.at<double>(j))));
}
}
else
{
alphas[k]=new_alpha;
L[k]=0.0;
}
k++;
}
l_inc=-2000000.0;
for(i=0; i<k; i++) if(L[i]>l_inc)
{
l_inc=L[i];
newAlpha=alphas[i];
}
}
//-------------------------------------------------------------------------------
Mat distSqrd(Mat& X,Mat& Y)
{
Mat D2;
int nx = X.rows;
int ny = Y.rows;
Mat xsq,ysq;
pow(X,2,xsq);
pow(Y,2,ysq);
Mat sumsqx;
cv::reduce(xsq,sumsqx,1,CV_REDUCE_SUM);
Mat sumsqy;
cv::reduce(ysq,sumsqy,1,CV_REDUCE_SUM);
D2 = sumsqx*Mat::ones(1,ny,CV_64FC1) + Mat::ones(nx,1,CV_64FC1)*sumsqy.t() - 2*(X*(Y.t()));
return D2;
}
Mat kernelFunction(Mat& X1,Mat& X2,double lenscal)
{
Mat K;
int N1=X1.rows;
int N2=X2.rows;
int d=X1.cols;
double eta = 1.0/pow(lenscal,2);
exp(-eta*distSqrd(X1,X2),K);
Mat K1=Mat(K.rows,K.cols+1,CV_64FC1);
K.copyTo(K1( Range(0,K.rows),Range(1,K1.cols)));
K1.col(0)=1;
return K1;
}
//output
// weights trained weights
// RV_idxs index into column of PHI of relevant basis
//input
// PHI basis function/design matrix
// t targetmatrix
// N number of training examples
// M number of basis functions
//[ N M] =size(PHI)
// P the number of target dimensions
// [ N P]= size(t)
// beta initial beta values for the target dimensions
// beta is set initially to for each target dimension p, beta_p=(1/(var(t_p))
void TrainRVM( Mat &X,Mat &t,double KernelWidth,int Max_It, Mat& beta,Mat &weights,Mat& RV_idxs,Mat& RV_X)
{
int N=X.rows;
int M=N+1;
int P=t.cols;
int i,j,p,k,MM;
const double INF=1e36;
beta=Mat (P,1,CV_64FC1);
Scalar mean,stddev;
// начальное приближение точности
for(int i=0;i<P;i++)
{
cv::meanStdDev(t.col(i),mean,stddev);
beta.at<double>(i)=1.0/(stddev[0]*stddev[0]+10.0*DBL_EPSILON);
}
Mat nonZero=Mat::zeros(M,1,CV_8UC1);
Mat PHI = kernelFunction(X,X,KernelWidth);
Mat PHIt;
PHIt=PHI.t()*t;
const double ALPHA_MAX=1e12;
Mat alpha(M,1,CV_64FC1);
alpha=ALPHA_MAX;
Mat gamma=Mat::ones(M,1,CV_64FC1);
bool run_cond;
Mat PHI2=PHI.t()*PHI;
Mat s(P,1,CV_64FC1);
Mat S(P,1,CV_64FC1);
Mat q(P,1,CV_64FC1);
Mat Q(P,1,CV_64FC1);
Mat l_inc(M,1,CV_64FC1);
Mat newAlpha(M,1,CV_64FC1);
double max_alpha, max_linc=-INF;
int max_index=-1;
int maxidx[2];
cv::minMaxIdx(l_inc,0,0,0,maxidx);
max_index=maxidx[0];
max_alpha=newAlpha.at<double>(max_index);
alpha.at<double>(max_index)=max_alpha;
//start the iterations
run_cond=true;
i=1;
while(run_cond)
{
MM=0;
for(j=0; j<M; j++)
{
if(alpha.at<double>(j)<ALPHA_MAX)
{
nonZero.at<unsigned char>(j)=true;
MM++;
}
else
{
nonZero.at<unsigned char>(j)=false;
}
}
Mat PHI_nz=Mat::zeros(N,MM,CV_64FC1);
Mat alpha_nz(MM,1,CV_64FC1);
k=0;
for(j=0; j<M; j++)
{
if(nonZero.at<unsigned char>(j))
{
alpha_nz.at<double>(k)=alpha.at<double>(j);
PHI.col(j).copyTo(PHI_nz.col(k));
k++;
}
}
vector<Mat> SIGMA_nz;
Mat HH=(PHI_nz.t()*PHI_nz);
for(p=0; p<P; p++)
{
Mat H=beta.at<double>(p)*HH;
H.diag()+=alpha_nz;
SIGMA_nz.push_back(H.inv(cv::DECOMP_SVD));
}
Mat dp_tmp;
Mat phi;
for(k=0; k<M; k++)
{
phi=PHI.col(k);
for(j=0; j<P; j++)
{
dp_tmp=beta.at<double>(j)*phi.t()*phi-beta.at<double>(j)*beta.at<double>(j)*phi.t()*PHI_nz*SIGMA_nz[j]*PHI_nz.t()*phi;
S.at<double>(j)=dp_tmp.at<double>(0);
dp_tmp=beta.at<double>(j)*phi.t()*t.col(j)-beta.at<double>(j)*beta.at<double>(j)*phi.t()*PHI_nz*SIGMA_nz[j]*PHI_nz.t()*t.col(j);
Q.at<double>(j)=dp_tmp.at<double>(0);
}
if(alpha.at<double>(k)<ALPHA_MAX)
{
s=alpha.at<double>(k)*S/(alpha.at<double>(k)-S);
q=alpha.at<double>(k)*Q/(alpha.at<double>(k)-S);
}
else
{
s=S.clone();
q=Q.clone();
}
SolveForAlpha(P,q,s,Q,S,alpha.at<double>(k),newAlpha.at<double>(k),l_inc.at<double>(k));
}
cv::minMaxIdx(l_inc,0,&max_linc,0,maxidx);
max_index=maxidx[0];
max_alpha=newAlpha.at<double>(max_index);
alpha.at<double>(max_index)=max_alpha;
weights=Mat(MM,P,CV_64FC1);
for(j=0; j<P; j++)
{
Mat tmp=beta.at<double>(j)*SIGMA_nz[j]*PHI_nz.t()*t.col(j);
tmp.copyTo(weights.col(j));
double gamma_sum=0.0;
gamma_sum=sum(1.0-alpha_nz.t()*SIGMA_nz[j].diag())[0];
Mat error=t.col(j)-PHI_nz*(weights.col(j));
pow(error,2,error);
double ED=0.0;
ED=sum(error)[0];
beta.at<double>(j)=(((double)N)- gamma_sum)/ED;
}
i++;
// Критерий выхода по количеству итераций или по максимальному
// изменению не превышающему заданный порог.
if(i>Max_It || max_linc<(100.0*DBL_EPSILON))
{
run_cond=false;
}
}
Mat nonZero_m=Mat(nonZero);
// Количество релевантных векторов
int nRVS=cv::countNonZero(nonZero_m);
// Индексы векторов
RV_idxs=Mat(nRVS,1,CV_32SC1);
// Координаты векторов (вторая координата по каждому измерению вычисляется)
RV_X=Mat(nRVS-1,1,CV_64FC1);
int ind=0;
for(int i=0;i<nonZero.rows;i++)
{
if(nonZero.at<unsigned char>(i))
{
RV_idxs.at<int>(ind)=i;
// первый индекс соответствует добавленной единице смещения
// поэтому начинаем со второго.
if(i>0)
{
RV_X.at<double>(ind-1)=X.at<double>(i);
}
ind++;
}
}
}
// -------------------------------------------------------------------
// Загрузка матриц. Для взаимодействия с матлабом во время отладки.
// -------------------------------------------------------------------
void ReadMat(ifstream& ifs,Mat& M)
{
int rows;
int cols;
ifs >> rows;
char comma;
ifs >> comma;
ifs >> cols;
M=Mat(rows,cols,CV_64FC1);
for(int i=0;i<rows;i++)
{
for(int j=0;j<cols;j++)
{
ifs >> M.at<double>(i,j);
if(j!=cols-1){ifs >> comma;}
}
}
}
// -------------------------------------------------------------------
// MATLAB matrix loading (for debug purpose)
// -------------------------------------------------------------------
Mat LoadMatrix(string filename)
{
Mat M;
ifstream ifs(filename);
if (ifs.is_open())
{
ReadMat(ifs,M);
ifs.close();
}
return M;
}
void PredictRVM(Mat& X,Mat& RV_X,Mat& weights,double KernelWidth,Mat& y_rvm)
{
Mat PHI=kernelFunction(X,RV_X,KernelWidth);
y_rvm=PHI*weights;
}
int main()
{
int gH=600;
int gW=600;
Mat graph=Mat::zeros(gH,gW,CV_8UC3);
namedWindow("graph");
Mat t=LoadMatrix("t.txt");
Mat X=LoadMatrix("X.txt");
for(int i=0;i<X.rows;i++)
{
circle(graph,Point(i*6,gW-(t.at<double>(i,0)+1)*160),2,Scalar(0,255,255),-1,CV_AA);
circle(graph,Point(i*6,gW-(t.at<double>(i,1)+1)*160),2,Scalar(0,255,255),-1,CV_AA);
}
imshow("graph",graph);
waitKey(10);
cout.precision(15);
Mat weights;
Mat RV_idxs;
Mat beta;
Mat RV_X;
double KernelWidth=4;
TrainRVM(X,t,KernelWidth,50, beta,weights,RV_idxs,RV_X);
COUT_VAR(weights);
Mat y_rvm;
PredictRVM(X,RV_X,weights,KernelWidth,y_rvm);
FileStorage fs("test.yml", FileStorage::WRITE);
fs << "weights" << weights;
fs << "RV_X" << RV_X;
fs.release();
for(int i=1;i<X.rows;i++)
{
Point2d p11(i*6,gW-(y_rvm.at<double>(i,0)+1)*160);
Point2d p21(i*6,gW-(y_rvm.at<double>(i,1)+1)*160);
i--;
Point2d p12(i*6,gW-(y_rvm.at<double>(i,0)+1)*160);
Point2d p22(i*6,gW-(y_rvm.at<double>(i,1)+1)*160);
i++;
line(graph,p11,p12,Scalar(255,255,0),1,CV_AA);
line(graph,p21,p22,Scalar(255,255,0),1,CV_AA);
}
imshow("graph",graph);
waitKey();
return 0;
}