A Comparative Study on Vector-based and Matrix-based Linear Discriminant Analysis

Recently a kind of matrix-based discriminant feature extraction approach called 2DLDA have been drawn much attention by researchers. 2DLDA can avoid the singularity problem and has low computational costs and has been experimentally reported that 2DLDA outperforms traditional LDA. In this paper, we compare 2DLDA with LDA in view of the discriminant power and find that 2DLDA as a kind of special LDA has no stronger discriminant power than LDA. So, why 2DLDA outperforms LDA in some cases? Through theoretical analysis, we find it is mainly because of the difference of stability under nonsingular linear transformation and linear operation power between 2DLDA and LDA. In experimental parts, the results of experiments give enough proof on our claims and show in some cases the performance of 2DLDA will be possible superior to that of LDA and in other cases the performance of LDA will be possible superior to that of 2DLDA.