Solution to generalized eigenvalue problem [generalized eigenvalue problem] [extended eigenvalue problem]

Recent exposure to LDA (linear discriminant analysis), LFDA (local discriminant analysis), Flda (Fisher linear discriminant analysis), MMDA (multi-modal discriminant analysis) and other methods for feature extraction, all of which involve the same problem--fisher The Criterion (Fisher discriminant criterion), which requires the minimization of intra-class discretization and the largest inter-class dispersion, describes the problem as shown in the figure:

This leads to the generalized eigenvalue problem, and for the solution of the problem, it is further converted to the eigenvalue and eigenvector of the asymmetric matrix (singular matrix) above, and to this step, the problem has been solved, in order to solve the eigenvalue and eigenvector of singular matrices, which is the singular matrix decomposition, for this problem, Matlab (Eig ()) and OpenCV (CVSVD ()) have given a good solution, the input to solve the singular matrix, the corresponding eigenvalues and eigenvectors are also obtained.

On the use of these functions, there are quite a lot of tutorials on the Internet, you slowly go ahead.