Sparse Coding for Symmetric Positive Definite Matrices with Application to Image Set Classification

Modelling videos or images with Symmetric Positive Definite (SPD) matrices and utilizing the intrinsic geometry of the Riemannian manifold has proven helpful for many computer vision tasks. Inspired by the significant success of sparse coding for vector data, recent researches show great interests in studying sparse coding for SPD matrices. However, the space of SPD matrices is a well-known Riemannian manifold so that existing sparse coding approaches for vector data cannot be directly extended. In this paper, we propose to use the Log-Euclidean Distance on the Riemannian manifold, which naturally derives a Riemannian kernel function to solve the sparse coding problem. The proposed method can be easily applied to image set classification by representing image sets with nonsingular covariance matrices. We compare our method with other sparse coding techniques for SPD matrices and demonstrate its benefits in image set classification on several standard datasets.