A unified tensor framework for face recognition

In this paper we propose a new optimization framework that unites some of the existing tensor based methods for face recognition on a common mathematical basis. Tensor based approaches rely on the ability to decompose an image into its constituent factors (i.e. person, lighting, viewpoint, etc.) and then utilizing these factor spaces for recognition. We first develop a multilinear optimization problem relating an image to its constituent factors and then develop our framework by formulating a set of strategies that can be followed to solve this optimization problem. The novelty of our research is that the proposed framework offers an effective methodology for explicit non-empirical comparison of the different tensor methods as well as providing a way to determine the applicability of these methods in respect to different recognition scenarios. Importantly, the framework allows the comparative analysis on the basis of quality of solutions offered by these methods. Our theoretical contribution has been validated by extensive experimental results using four benchmark datasets which we present along with a detailed discussion.