Learning Discriminative αβ-Divergences for Positive Definite Matrices

A. Cherian, P. Stanitsas, M. Harandi, V. Morellas, N. Papanikolopoulos

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Scopus citations


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 αß-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.

Original languageEnglish (US)
Title of host publicationProceedings - 2017 IEEE International Conference on Computer Vision, ICCV 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages10
ISBN (Electronic)9781538610329
StatePublished - Dec 22 2017
Event16th IEEE International Conference on Computer Vision, ICCV 2017 - Venice, Italy
Duration: Oct 22 2017Oct 29 2017

Publication series

NameProceedings of the IEEE International Conference on Computer Vision
ISSN (Print)1550-5499


Other16th IEEE International Conference on Computer Vision, ICCV 2017


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