  Symmetric positive definite (SPD) matrices are useful for capturing
second-order statistics of visual data. To compare two SPD matrices, several
measures are available, such as the affine-invariant Riemannian metric,
Jeffreys divergence, Jensen-Bregman logdet divergence, etc.; however, their
behaviors may be application dependent, raising the need of manual selection to
achieve the best possible performance. Further and as a result of their
overwhelming complexity for large-scale problems, computing pairwise
similarities by clever embedding of SPD matrices is often preferred to direct
use of the aforementioned measures. In this paper, we propose a discriminative
metric learning framework, Information Divergence and Dictionary Learning
(IDDL), that not only learns application specific measures on SPD matrices
automatically, but also embeds them as vectors using a learned dictionary. To
learn the similarity measures (which could potentially be distinct for every
dictionary atom), we use the recently introduced alpha-beta-logdet divergence,
which is known to unify the measures listed above. We propose a novel IDDL
objective, that learns the parameters of the divergence and the dictionary
atoms jointly in a discriminative setup and is solved efficiently using
Riemannian optimization. We showcase extensive experiments on eight computer
vision datasets, demonstrating state-of-the-art performances.
