Classification of symmetric positive definite matrices based on bilinear isometric Riemannian embedding

Abstract

Because covariance features with the form of symmetric positive definite matrices lie on Riemannian manifold, classification on Riemannian manifold could possess high performance in many applications. Unfortunately, the applicability of classification methods developed on Riemannian manifold is limited by their huge computational complexities, particularly with the feature data on high-dimensional Riemannian manifold. To alleviate the problem of computational cost, in this paper, a simple yet efficient dimensionality reduction algorithm, bilinear isometric Riemannian embedding, is derived to construct a low-dimensional embedding from high-dimensional Riemannian manifold. To this end, we model the bilinear isometric mapping to identify a low-dimensional embedding that maximizes the preservation of Riemannian geodesic distance. A supervised classification method, embedding discriminant analysis, is then proposed based on the low-dimensional embedding. Experimental results on image and electroencephalogram reveal that the proposed algorithms can efficiently extract the distance-preserving embedding and obtain higher classification performance.