Fractional order singular value decomposition representation for face recognition

Face Representation (FR) plays a typically important role in face recognition and methods such as Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA) have been received wide attention recently. However, despite of the achieved successes, these FR methods will inevitably lead to poor classification performance in case of great facial variations such as expression, lighting, occlusion and so on, due to the fact that the image gray value matrices on which they manipulate are very sensitive to these facial variations. In this paper, we take notice of the facts that every image matrix can always have the well-known Singular Value Decomposition (SVD) and can be regarded as a composition of a set of base images generated by SVD, and we further point out that the leading base images (those corresponding to large singular values) on one hand are sensitive to the aforementioned facial variations and on the other hand dominate the composition of the face image. Then based on these observations, we subtly deflate the weights of the facial variation sensitive base images by a parameter α and propose a novel Fractional order Singular Value Decomposition Representation (FSVDR) to alleviate facial variations for face recognition. Finally, our experimental results show that FSVDR can: 1) effectively alleviate facial variations; and 2) form an intermediate representation for many FR methods such as PCA and LDA to significantly improve their classification performance in case of great facial variations.