NDLI: Rolling Riemannian Manifolds to Solve the Multi-class Classification Problem

Content Provider	IEEE Xplore Digital Library
Author	Caseiro, R. Martins, P. Henriques, J.F. Silva Leite, F. Batista, J.
Copyright Year	2013
Description	Author affiliation: Inst. of Syst. & Robot., Univ. of Coimbra, Coimbra, Portugal (Caseiro, R.; Martins, P.; Henriques, J.F.; Silva Leite, F.; Batista, J.)
Abstract	In the past few years there has been a growing interest on geometric frameworks to learn supervised classification models on Riemannian manifolds [32, 28]. A popular framework, valid over any Riemannian manifold, was proposed in [32] for binary classification. Once moving from binary to multi-class classification this paradigm is not valid anymore, due to the spread of multiple positive classes on the manifold [28]. It is then natural to ask whether the multi-class paradigm could be extended to operate on a large class of Riemannian manifolds. We propose a mathematically well-founded classification paradigm that allows to extend the work in [32] to multi-class models, taking into account the structure of the space. The idea is to project all the data from the manifold onto an affine tangent space at a particular point. To mitigate the distortion induced by local diffeomorphisms, we introduce for the first time in the computer vision community a well-founded mathematical concept, so-called Rolling map [22, 17]. The novelty in this alternate school of thought is that the manifold will be firstly rolled (without slipping or twisting) as a rigid body, then the given data is unwrapped onto the affine tangent space, where the classification is performed.
Starting Page	41
Ending Page	48
File Size	493877
Page Count	8
File Format	PDF
ISBN	9780769549897
ISSN	10636919
DOI	10.1109/CVPR.2013.13
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2013-06-23
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Manifolds Symmetric matrices Kernel Computer vision Educational institutions Extraterrestrial measurements Object Classification Riemannian Manifolds Rolling motions
Content Type	Text
Resource Type	Article
Subject	Computer Vision and Pattern Recognition Software

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