void PCA::kernel_pca(MatrixXd & dataPoints, unsigned int dimSpace)
{
int m = dataPoints.rows();
int n = dataPoints.cols();
sourcePoints = dataPoints;
if(k) delete k;
switch(kernelType)
{
case 0:
k = new LinearKernel();
break;
case 1:
k = new PolyKernel(degree);
break;
case 2:
k = new RBFKernel(gamma);
break;
default:
k = new Kernel();
}
k->Compute(dataPoints);
//std::cout << "K:\n" << k->get() << "\n";
// ''centralize''
MatrixXd K_Centralized = k->get()
- MatrixXd::Ones(n, n)*k->get()
- k->get()*MatrixXd::Ones(n, n)
+ MatrixXd::Ones(n, n)*k->get()*MatrixXd::Ones(n, n);
//std::cout << "Centralized" << "\n";
//std::cout << "K:\n" << k->get() << "\n";
// compute the eigenvalue on the K_Centralized Matrix
EigenSolver<MatrixXd> m_solve(K_Centralized);
//std::cout << "got the eigenvalues, eigenvectors" << "\n";
eigenvalues = m_solve.eigenvalues().real();
eigenVectors = m_solve.eigenvectors().real();
//std::cout << "eigv:\n" << eigenvalues << "\n";
//std::cout << "eigs:\n" << eigenVectors << "\n";
// sort and get the permutation indices
pi.clear();
for (int i = 0 ; i < n; i++)
pi.push_back(std::make_pair(-eigenvalues(i), i));
std::sort(pi.begin(), pi.end());
// get top eigenvectors
_result = MatrixXd::Zero(n, dimSpace);
for (unsigned int i = 0; i < dimSpace; i++)
{
_result.col(i) = eigenVectors.col(pi[i].second); // permutation indices
}
MatrixXd sqrtE = MatrixXd::Zero(dimSpace, dimSpace);
for (unsigned int i = 0; i < dimSpace; i++)
{
//sqrtE(i, i) = sqrt(-pi[i].first);
sqrtE(i, i) = 0.9;
}
// get the final data projection
_result = (sqrtE * _result.transpose()).transpose();
}
int main( void) {
FILE *fp;
MATRIX_T *a, *b, *c, *d, *inverse, *test, *x, *ainv;
double D;
/* initialize all MATRIX_T pointers to NULL */
a = NULL;
b = NULL;
c = NULL;
d = NULL;
inverse = NULL;
test = NULL;
x = NULL;
ainv = NULL;
/* it is good practice to reset the error code
before doing matrix calculations */
m_reseterr();
/* open matrix file to initialize matrix variables */
if ((fp = fopen("mtest1.mat","r"))==NULL) {
printf("cannot open file mtest1.mat\n");
exit(0);
}
/* use m_printf functions here */
/* test matrix addition */
a = m_fnew( fp);
m_printf( "\n# matrix a from file: mtest1.mat", "%6.2f", a);
b = m_fnew( fp);
m_printf( "\n# matrix b from: mtest1.mat", "%6.2f", b);
c = m_new( 3, 2);
c = m_add( c, a, b);
m_printf( "\n# sum of a and b", "%6.2f", c);
/* test matrix subtraction */
c = m_sub( c, a, b);
m_printf( "\n# difference of a and b", "%6.2f", c);
/* change to using comma separated format output */
/* multiply matrix by a constant */
printf( "\ncomma separated format: matrix a\n");
m_fputcsv(stdout,a);
printf( "\ncomma separated format: matrix c\n");
m_fputcsv(stdout,c);
m_mupconst( c, 2.5, a);
printf( "\ncsv format: 2.5 times matrix c\n");
m_fputcsv(stdout,c);
/* find maximum element in matrix */
printf( "\nmax element in c is %f\n", m_max_abs_element(c));
/* test euclidean norm */
d = m_fnew( fp);
printf( "\ncsv format: matrix d\n");
m_fputcsv(stdout,d);
printf( "\neuclidean norm of d is %f\n", m_e_norm( d));
/* test assignment of identity matrix to a square matrix */
inverse = m_new( d->rows, d->cols);
m_assign_identity( inverse);
m_printf( "\nidentity matrix", "%6.2f", inverse);
/* test matrix inversion */
inverse = m_inverse( inverse, d, &D, 0.0001);
test = m_new(d->rows,d->cols);
test = m_mup( test, d, inverse);
m_printf( "\nmatrix d", "%6.2f", d);
m_printf( "\nmatrix inverse", "%6.2f", inverse);
m_printf( "\nproduct of d and d-inverse", "%6.2f", test);
/* test solution of linear equations */
/* start by getting new values for matrices a and b
note: b is a 1 by n vector (as is x) */
if ((a = m_fnew( fp)) == NULL) exit(0);
if ((b = m_fnew( fp)) == NULL) exit(0);
if ((x = m_new(b->rows,b->cols)) == NULL) exit(0);
printf("\ncsv: a\n");
m_fputcsv(stdout,a);
printf("\ncsv: b\n");
m_fputcsv(stdout,b);
x = m_solve( x, a, b, 0.0000001);
printf("\n\nx=ab\ncsv: solution x\n");
m_fputcsv(stdout,x);
/* close files and clean up */
fclose(fp);
m_free(a);
m_free(b);
m_free(c);
m_free(d);
m_free(inverse);
m_free(test);
m_free(x);
m_free(ainv);
}
