Singular Value Decomposition Projection for solving the small sample size problem in face recognition

Numerous dimensionality reduction methods have achieved impressive performance in face recognition field due to their potential to exploit the intrinsic structure of images and to enhance the computational efficiency. However, the FR methods based on the existing dimensionality reduction often suffer from small sample size (SSS) problems, where the sample dimensionality is larger than the number of training samples per subject. In recent years, Sparse Representation based Classification (SRC) has been demonstrated to be a powerful framework for robust FR. In this paper, a novel unsupervised dimensionality reduction algorithm, called Singular Value Decomposition Projection (SVDP), is proposed to better fit SRC for handling the SSS problems in FR. In SVDP, a weighted linear transformation matrix is derived from the original data matrix via Singular Value Decomposition. The projection obtained in this way is row-orthonormal and it has some good properties. It makes the solution be robust to small perturbations contained in the data and has better ability to represent various signals. Thus, SVDP could better preserve the discriminant information of the data. Based on SVDP, a novel face recognition method SVDP-SRC is designed to enable SRC to achieve better performance via low-dimensional representation of faces. The experiments carried out with some simulated data show that SVDP achieves higher recovery accuracy than several other dimensionality reduction methods. Moreover, the results obtained on three standard face databases demonstrate that SVDP-SRC is quite effective to handle the SSS problems in terms of recognition accuracy.