Geodesic Discriminant Analysis on Curved Riemannian Manifold

In this paper, we present a geodesic discriminant analysis (GDA) algorithm, which generalize linear discriminant analysis (LDA) in linear manifold space to curved Riemannian manifold space, with the aid of Riemannian logarithmic map. Compared with LDA, GDA is more suitable to deal with data that lie on curved manifold. We show that GDA is the generalization of LDA, and LDA is the special case of GDA: GDA equals to the data-centralized LDA when the underlying manifold is a linear manfold. Experimental results on facial needle-map data show the superiority of GDA over LDA when data lie on curved manifold.