  This paper introduces sparse coding and dictionary learning for Symmetric
Positive Definite (SPD) matrices, which are often used in machine learning,
computer vision and related areas. Unlike traditional sparse coding schemes
that work in vector spaces, in this paper we discuss how SPD matrices can be
described by sparse combination of dictionary atoms, where the atoms are also
SPD matrices. We propose to seek sparse coding by embedding the space of SPD
matrices into Hilbert spaces through two types of Bregman matrix divergences.
This not only leads to an efficient way of performing sparse coding, but also
an online and iterative scheme for dictionary learning. We apply the proposed
methods to several computer vision tasks where images are represented by region
covariance matrices. Our proposed algorithms outperform state-of-the-art
methods on a wide range of classification tasks, including face recognition,
action recognition, material classification and texture categorization.
