What is the underlying relationship between unilateral two-dimensional LDA and block-based LDA?

Although it has been verified that unilateral two-dimensional linear discriminant analysis (U2DLDA) is not identical with a special case of block-based LDA, the underlying relationship between U2DLDA and block-based LDA stays open. Here we find that U2DLDA on one training set is equivalent to the special case of block-based LDA on another training set, where each class of centered 2D samples in the former set is divided into n subclasses corresponding to n columns (rows) of the 2D samples. Furthermore, a reasonable interpretation why U2DLDA potentially outperforms the special case of block-based LDA and the corresponding experimental results based on Yale and ORL face databases are given.