Clustering Positive Definite Matrices by Learning Information Divergences

Panagiotis Stanitsas, Anoop Cherian, Vassilios Morellas, Nikolaos Papanikolopoulos

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

Abstract

Data representations based on Symmetric Positive Definite (SPD) matrices are gaining popularity in visual learning applications. When comparing SPD matrices, measures based on non-linear geometries often yield beneficial results. However, a manual selection process is commonly used to identify the appropriate measure for a visual learning application. In this paper, we study the problem of clustering SPD matrices while automatically learning a suitable measure. We propose a novel formulation that jointly (i) clusters the input SPD matrices in a K-Means setup and (ii) learns a suitable non-linear measure for comparing SPD matrices. For (ii), we capitalize on the recently introduced αβ-logdet divergence, which generalizes a family of popular similarity measures on SPD matrices. Our formulation is cast in a Riemannian optimization framework and solved using a conjugate gradient scheme. We present experiments on five computer vision datasets and demonstrate state-of-the-art performance.

Original languageEnglish (US)
Title of host publicationProceedings - 2017 IEEE International Conference on Computer Vision Workshops, ICCVW 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1304-1312
Number of pages9
ISBN (Electronic)9781538610343
DOIs
StatePublished - Jul 1 2017
Event16th IEEE International Conference on Computer Vision Workshops, ICCVW 2017 - Venice, Italy
Duration: Oct 22 2017Oct 29 2017

Publication series

NameProceedings - 2017 IEEE International Conference on Computer Vision Workshops, ICCVW 2017
Volume2018-January

Other

Other16th IEEE International Conference on Computer Vision Workshops, ICCVW 2017
CountryItaly
CityVenice
Period10/22/1710/29/17

Bibliographical note

Funding Information:
This material is based upon work supported by the National Science Foundation through grants #CNS-0934327, #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).

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