The multifactor extension of Grassmann manifolds for face recognition

We propose the use of a multifactor model that extends Grassmann manifold to multiple factor frameworks. Both manifold learning algorithms and multifactor analysis are state-of-the-art dimension reduction techniques that are suitable to model variations of face images. In this paper, we demonstrate that Grassmann manifold can be extended to Mul-tifactor Grassmann manifold when used in conjunction with Multilinear PCA (MPCA). Indeed, the multifactor manifold learning algorithm proposed in this paper can be interpreted as MPCA´s kernel-based extension using a kernel function that is defined in terms of geodesic distance. As a result, we first propose the use of Multifactor Grassmann manifold, which can learn both a multifactor structure and an underlying manifold in a given set of face images. We then demonstrate that our proposed method, Multifactor Grassmann manifold, produces more reliable results in the context of face recognition than the traditional dimension reduction techniques.