DLDA and LDA/QR equivalence framework for human face recognition

Singularity problem in human face feature extraction is very challenging that has gained a lot of attentions during the last decade. A pseudo-inverse linear discriminant analysis (LDA) plays a important role to solve the singularity problem of the scatter matrices. In this paper, we make use of Linear Discriminant Analysis via QR decomposition (LDA/QR) and Direct Linear Discriminant Analysis (DLDA) to solve the singularity problem in face feature recognition. We also show that an equivalent relationship between DLDA and LDA/QR. They can be regarded as a special case of pseudo-inverse LDA. Similar to LDA/QR algorithm, DLDA could be a two-stage LDA method. Interestingly, we find that the first stage of DLDA can act as a dimensionality reduction algorithm. In our experiment, we compare DLDA and LDA/QR algorithms in terms of classification accuracy, computational complexity in ORL and Yale face datasets. We have also conducted experiments to compare their first stages on these datasets. Our results indicate that the empirical and theoretic proofs of equivalence between DLDA and LDA/QR algorithms coincidentally converge and verify their same capabilities in the dimension reduction.