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

Sparse Coding on Symmetric Positive Definite Manifolds using Bregman Divergences