Geometric Data Analysis Based on Manifold Learning with Applications for Image Understanding

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dc.contributor.authorMIRANDA, G. F.
dc.contributor.authorPlinio Thomaz Aquino Junior
dc.contributor.authorGIRALDI, G. A.
dc.contributor.authorOrcidhttps://orcid.org/0000-0002-5100-7443
dc.date.accessioned2022-01-12T21:58:03Z
dc.date.available2022-01-12T21:58:03Z
dc.date.issued2017-07-01
dc.description.abstract© 2017 IEEE.Nowadays, pattern recognition, computer vision, signal processing and medical image analysis, require the managing of large amount of multidimensional image databases, possibly sampled from nonlinear manifolds. The complex tasks involved in the analysis of such massive data lead to a strong demand for nonlinear methods for dimensionality reduction to achieve efficient representation for information extraction. In this avenue, manifold learning has been applied to embed nonlinear image data in lower dimensional spaces for subsequent analysis. The result allows a geometric interpretation of image spaces with relevant consequences for data topology, computation of image similarity, discriminant analysis/classification tasks and, more recently, for deep learning issues. In this paper, we firstly review Riemannian manifolds that compose the mathematical background in this field. Such background offers the support to set up a data model that embeds usual linear subspace learning and discriminant analysis results in local structures built from samples drawn from some unknown distribution. Afterwards, we discuss topological issues in data preparation for manifold learning algorithms as well as the determination of manifold dimension. Then, we survey dimensionality reduction techniques with particular attention to Riemannian manifold learning. Besides, we discuss the application of concepts in discrete and polyhedral geometry for synthesis and data clustering over the recovered Riemannian manifold with emphasis in face images in the computational experiments. Next, we discuss promising perspectives of manifold learning and related topics for image analysis, classification and relationships with deep learning methods. Specifically, we discuss the application of foliation theory, discriminant analysis and kernel methods in curved spaces. Besides, we take differential geometry in manifolds as a paradigm to discuss deep generative models and metric learning algorithms.
dc.description.firstpage42
dc.description.lastpage62
dc.description.volume2018-January
dc.identifier.citationMIRANDA, G. F.; AQUINO JUNIOR, P. T.; GIRALDI, G. A. Geometric Data Analysis Based on Manifold Learning with Applications for Image Understanding. Proceedings - 2017 30th SIBGRAPI Conference on Graphics, Patterns and Images Tutorials SIBGRAPI-T 2017, v. 2018-January, p. 42-62, jul. 2017.
dc.identifier.doi10.1109/SIBGRAPI-T.2017.9
dc.identifier.urihttps://repositorio.fei.edu.br/handle/FEI/3835
dc.relation.ispartofProceedings - 2017 30th SIBGRAPI Conference on Graphics, Patterns and Images Tutorials SIBGRAPI-T 2017
dc.rightsAcesso Restrito
dc.subject.otherlanguagedeep learning
dc.subject.otherlanguageimage analysis
dc.subject.otherlanguagemanifold learning
dc.subject.otherlanguageRiemannian manifolds
dc.subject.otherlanguagestatistical learning
dc.titleGeometric Data Analysis Based on Manifold Learning with Applications for Image Understanding
dc.typeArtigo de evento
fei.scopus.citations7
fei.scopus.eid2-s2.0-85050219202
fei.scopus.subjectComputational experiment
fei.scopus.subjectDimensionality reduction
fei.scopus.subjectDimensionality reduction techniques
fei.scopus.subjectManifold learning
fei.scopus.subjectManifold learning algorithm
fei.scopus.subjectMulti-dimensional images
fei.scopus.subjectRiemannian manifold
fei.scopus.subjectStatistical learning
fei.scopus.updated2024-07-01
fei.scopus.urlhttps://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85050219202&origin=inward
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