/**
eigentrain
computes the eigen space for matrix images.
This function is used in the training procedure of the face recognition pca
algorithm.
INPUT: the data matrix of images
OUTPUT: mean: the mean value of the images
eigen_values: eigenvalues
eigen_base: eigenvectors
The data matrix is mean centered, and this is a side effect.
*/
void eigentrain(Matrix *mean, Matrix *eigen_vals,
Matrix *eigen_base, Matrix images)
{
double p = 0.0;
Matrix M, eigenvectors;
DEBUG(1, "Calculating mean image.");
*mean = get_mean_image(images);
DEBUG(1, "Calculating the mean centered images for the training set.");
mean_subtract_images(images, *mean);
MESSAGE2ARG("Calculating Covariance Matrix: M = images' * images. M is a %d by %d Matrix.", images->col_dim, images->col_dim);
M = transposeMultiplyMatrixL(images, images);
DEBUG_INT(3, "Covariance Matrix Rows", M->row_dim);
DEBUG_INT(3, "Covariance Matrix Cols", M->col_dim);
DEBUG(2, "Allocating memory for eigenvectors and eigenvalues.");
eigenvectors = makeMatrix(M->row_dim, M->col_dim);
*eigen_vals = makeMatrix(M->row_dim, 1);
MESSAGE("Computing snap shot eigen vectors using the double precision cv eigensolver.");
cvJacobiEigens_64d(M->data, eigenvectors->data, (*eigen_vals)->data, images->col_dim, p, 1);
freeMatrix(M);
DEBUG(1, "Verifying the eigen vectors");
/* Reconstruct M because it is destroyed in cvJacobiEigens */
M = transposeMultiplyMatrixL(images, images);
if (debuglevel >= 3)
eigen_verify(M, *eigen_vals, eigenvectors);
freeMatrix(M);
*eigen_base = multiplyMatrix(images, eigenvectors);
MESSAGE2ARG("Recovered the %d by %d high resolution eigen basis.", (*eigen_base)->row_dim, (*eigen_base)->col_dim);
DEBUG(1, "Normalizing eigen basis");
basis_normalize(*eigen_base);
/*Remove last elements because they are unneeded. Mean centering the image
guarantees that the data points define a hyperplane that passes through
the origin. Therefore all points are in a k - 1 dimensional subspace.
*/
(*eigen_base)->col_dim -= 1;
(*eigen_vals)->row_dim -= 1;
eigenvectors->col_dim -= 1;
DEBUG(1, "Verifying eigenbasis");
if (debuglevel >= 3)
basis_verify(images, *eigen_base);
/* The eigenvectors for the smaller covariance (snap shot) are not needed */
freeMatrix(eigenvectors);
}
/* findBCSMatrix
The approach here is to use equation 116 on p. 122 of
Duda, "Pattern Classification" to solve for the between
class scatter matrix. The equation reads:
St = Sw + Sb (St is total scatter matrix)
Solving for Sb, Sb = St - Sw. Note Sw is computed above.
The total scatter matrix is easy to compute, it is what we
think of as the covariance matrix when the points have been
centered.
*/
Matrix findBCSMatrix(Matrix imspca, Matrix Sw) {
Matrix Sb;
Matrix St;
Matrix mean;
MESSAGE("Finding between-class scatter matrix.");
mean = get_mean_image(imspca);
mean_subtract_images(imspca, mean);
DEBUG(3, "Producing total scatter matrix");
St = transposeMultiplyMatrixR(imspca, imspca);
DEBUG(2, "Producing between-class scatter matrix");
Sb = subtractMatrix(St, Sw);
freeMatrix(St);
freeMatrix(mean);
return Sb;
}