An improved kernel discriminate analysis on grassmannian manifold for face recognition

Abstract

Accompany with the understanding for geometry structure of manifold, more and more people used the Grassmannian manifold to face recognition via image sets. In order to improve the accuracy of recognition, several studies applied the discriminant analysis on such manifolds. However, most of these methods suffer from not considering the local structure of the manifold data. Accounting for success of the Symmetric Positive Definite (SPD) matrices in many algorithms, an improved method of discriminant analysis on Grassmannian manifold has been proposed in this paper. Similar to the conventional method, our approach map the SPD matrices to a high dimensional Hilbert space where Euclidean geometry applies also. With the Grassmannian kernel function which derived from Gaussian kernel use the different metric for Riemannian manifold of SPD matrices, the local geometry of mapping can be considered. The graph embedding on new feature space can get a better performance than conventional methods. Experiments on CMU PIE and BANCA databases demonstrate the efficient of our method.