Skip navigation
Skip navigation

From manifold to manifold: Geometry-aware dimensionality reduction for SPD matrices

Harandi, Mehrtash; Salzmann, Mathieu; Hartley, Richard

Description

Representing images and videos with Symmetric Positive Definite (SPD) matrices and considering the Riemannian geometry of the resulting space has proven beneficial for many recognition tasks. Unfortunately, computation on the Riemannian manifold of SPD matrices -especially of high-dimensional ones- comes at a high cost that limits the applicability of existing techniques. In this paper we introduce an approach that lets us handle high-dimensional SPD matrices by constructing a...[Show more]

dc.contributor.authorHarandi, Mehrtash
dc.contributor.authorSalzmann, Mathieu
dc.contributor.authorHartley, Richard
dc.coverage.spatialZurich Switzerland
dc.date.accessioned2015-12-13T22:31:33Z
dc.date.available2015-12-13T22:31:33Z
dc.date.createdSeptember 6-12 2014
dc.identifier.isbn9783319106045
dc.identifier.urihttp://hdl.handle.net/1885/75304
dc.description.abstractRepresenting images and videos with Symmetric Positive Definite (SPD) matrices and considering the Riemannian geometry of the resulting space has proven beneficial for many recognition tasks. Unfortunately, computation on the Riemannian manifold of SPD matrices -especially of high-dimensional ones- comes at a high cost that limits the applicability of existing techniques. In this paper we introduce an approach that lets us handle high-dimensional SPD matrices by constructing a lower-dimensional, more discriminative SPD manifold. To this end, we model the mapping from the high-dimensional SPD manifold to the low-dimensional one with an orthonormal projection. In particular, we search for a projection that yields a low-dimensional manifold with maximum discriminative power encoded via an affinity-weighted similarity measure based on metrics on the manifold. Learning can then be expressed as an optimization problem on a Grassmann manifold. Our evaluation on several classification tasks shows that our approach leads to a significant accuracy gain over state-of-the-art methods.
dc.publisherSpringer Verlag
dc.relation.ispartofseries13th European Conference on Computer Vision, ECCV 2014
dc.sourceLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
dc.titleFrom manifold to manifold: Geometry-aware dimensionality reduction for SPD matrices
dc.typeConference paper
local.description.notesImported from ARIES
local.description.refereedYes
dc.date.issued2014
local.identifier.absfor080100 - ARTIFICIAL INTELLIGENCE AND IMAGE PROCESSING
local.identifier.ariespublicationU3488905xPUB4562
local.type.statusPublished Version
local.contributor.affiliationHarandi, Mehrtash, College of Engineering and Computer Science, ANU
local.contributor.affiliationSalzmann, Mathieu, College of Engineering and Computer Science, ANU
local.contributor.affiliationHartley, Richard, College of Engineering and Computer Science, ANU
local.bibliographicCitation.startpage17
local.bibliographicCitation.lastpage32
local.identifier.doi10.1007/978-3-319-10605-2_2
local.identifier.absseo970108 - Expanding Knowledge in the Information and Computing Sciences
dc.date.updated2015-12-11T09:01:23Z
local.identifier.scopusID2-s2.0-84906500891
CollectionsANU Research Publications

Download

There are no files associated with this item.


Items in Open Research are protected by copyright, with all rights reserved, unless otherwise indicated.

Updated:  22 January 2019/ Responsible Officer:  University Librarian/ Page Contact:  Library Systems & Web Coordinator