Abstract

In video based face recognition, great success has been made by representing videos as linear subspaces, which typically lie in a special type of non-Euclidean space known as Grassmann manifold. To leverage the kernel-based methods developed for Euclidean space, several recent methods have been proposed to embed the Grassmann manifold into a high dimensional Hilbert space by exploiting the well established Project Metric, which can approximate the Riemannian geometry of Grassmann manifold. Nevertheless, they inevitably introduce the drawbacks from traditional kernel-based methods such as implicit map and high computational cost to the Grassmann manifold. To overcome such limitations, we propose a novel method to learn the Projection Metric directly on Grassmann manifold rather than in Hilbert space. From the perspective of manifold learning, our method can be regarded as performing a geometry-aware dimensionality reduction from the original Grassmann manifold to a lower-dimensional, more discriminative Grassmann manifold where more favorable classification can be achieved. Experiments on several real-world video face datasets demonstrate that the proposed method yields competitive performance compared with the state-ofthe-art algorithms.