Dimensionality Reduction on Grassmannian: A Good Practice

Abstract

Representing images and videos as linear subspaces for visual recognition has made a great success which benefits from the Riemannian geometry named the Grassmann manifold. However, subspaces in vision are high-dimensional, which leads to a high computational expense and limited applicability of existing techniques. In this paper, we propose a generalized model to learn a lower-dimensional and more discriminative Grassmann manifold from the high dimensional one through an orthonormal projection for a better classification. We respect the Riemannian geometry of the Grassmann manifold and search for this projection directly from one Grassmann manifold to another face-to-face without any additional transformations. In this natural geometry-aware way, any metric on the Grassmann manifold can be resided in our model theoretically. We have combined different metrics with our model and the learning process can be treated as an unconstrained optimization problem on a Grassmann manifold. Experiments on several action datasets demonstrate that our approach can improve a more favorable accuracy over the state-of-the-art algorithms.