Cherian, AnoopStanitsas, PanagiotisHarandi, MehrtashMorellas, VassiliosPapanikolopoulos, NikolaosO'Conner, Lisa2024-05-06October 22978-1-5386-1032-9http://hdl.handle.net/1885/317298Symmetric 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.This material is based upon work supported by the National Science Foundation through grants #CNS0934327, #CNS-1039741, #SMA-1028076, #CNS-1338042, #CNS-1439728, #OISE-1551059, and #CNS-1514626. AC is funded by the Australian Research Council Centre of Excellence for Robotic Vision (#CE140100016).application/pdfen-AU© 2017 IEEE201710.1109/ICCV.2017.4582023-01-08