Sparse representation based classification with intra-class variation dictionary on symmetric positive definite manifolds

Sparse representation based classification (SRC) using training samples as a dictionary has engendered promising results for many computer vision tasks. However, although the SRC classifier exhibits very competitive performances when given sufficient training samples of each class, it presents the difficulty that its performance decreases considerably when fewer training samples are used. As described herein, we propose a Riemannian SRC with intra-class variation dictionary on SPD matrices, R-ESRC. The key challenge is establishment of a mathematically correct intra-class variation dictionary in terms of geometry of SPD manifold. To this end, we exploit the geometric mean calculation and the logarithm mapping. Numerical evaluations demonstrate the superior performance of our proposed algorithm.