Discriminant Analysis on Riemannian Manifold of Gaussian Distributions for Face Recognition With Image Sets

To address the problem of face recognition with image sets, we aim to capture the underlying data distribution in each set and thus facilitate more robust classification. To this end, we represent image set as the Gaussian mixture model (GMM) comprising a number of Gaussian components with prior probabilities and seek to discriminate Gaussian components from different classes. Since in the light of information geometry, the Gaussians lie on a specific Riemannian manifold, this paper presents a method named discriminant analysis on Riemannian manifold of Gaussian distributions (DARG). We investigate several distance metrics between Gaussians and accordingly two discriminative learning frameworks are presented to meet the geometric and statistical characteristics of the specific manifold. The first framework derives a series of provably positive definite probabilistic kernels to embed the manifold to a high-dimensional Hilbert space, where conventional discriminant analysis methods developed in Euclidean space can be applied, and a weighted Kernel discriminant analysis is devised which learns discriminative representation of the Gaussian components in GMMs with their prior probabilities as sample weights. Alternatively, the other framework extends the classical graph embedding method to the manifold by utilizing the distance metrics between Gaussians to construct the adjacency graph, and hence the original manifold is embedded to a lower-dimensional and discriminative target manifold with the geometric structure preserved and the interclass separability maximized. The proposed method is evaluated by face identification and verification tasks on four most challenging and largest databases, YouTube Celebrities, COX, YouTube Face DB, and Point-and-Shoot Challenge, to demonstrate its superiority over the state-of-the-art.To address the problem of face recognition with image sets, we aim to capture the underlying data distribution in each set and thus facilitate more robust classification. To this end, we represent image set as the Gaussian mixture model (GMM) comprising a number of Gaussian components with prior probabilities and seek to discriminate Gaussian components from different classes. Since in the light of information geometry, the Gaussians lie on a specific Riemannian manifold, this paper presents a method named discriminant analysis on Riemannian manifold of Gaussian distributions (DARG). We investigate several distance metrics between Gaussians and accordingly two discriminative learning frameworks are presented to meet the geometric and statistical characteristics of the specific manifold. The first framework derives a series of provably positive definite probabilistic kernels to embed the manifold to a high-dimensional Hilbert space, where conventional discriminant analysis methods developed in Euclidean space can be applied, and a weighted Kernel discriminant analysis is devised which learns discriminative representation of the Gaussian components in GMMs with their prior probabilities as sample weights. Alternatively, the other framework extends the classical graph embedding method to the manifold by utilizing the distance metrics between Gaussians to construct the adjacency graph, and hence the original manifold is embedded to a lower-dimensional and discriminative target manifold with the geometric structure preserved and the interclass separability maximized. The proposed method is evaluated by face identification and verification tasks on four most challenging and largest databases, YouTube Celebrities, COX, YouTube Face DB, and Point-and-Shoot Challenge, to demonstrate its superiority over the state-of-the-art.