Theory analysis on FSLDA and ULDA

It is first revealed that the Fisher criterion ratio of each FSLDA discriminant vector must not be less than that of corresponding ULDA discriminant vector. So, the phenomenon in Yang et al. (Pattern Recognition 35 (2002) 2665) is not strange but certain, and must be available in all experiments! In addition, it is also first illustrated that in fact ULDA discriminant vectors are the S_t? orthogonal eigenvectors of a generalized eigenequation. As a result, the algorithms to obtain S_t? orthogonal eigenvectors of the generalized eigenequation are equivalent to the ULDA algorithm. Consequently, it is possible to work out ULDA discriminant vectors more efficiently.