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1. Identity statement
Reference TypeConference Paper (Conference Proceedings)
Sitesibgrapi.sid.inpe.br
Holder Codeibi 8JMKD3MGPEW34M/46T9EHH
Identifier8JMKD3MGPAW/3PJRSSH
Repositorysid.inpe.br/sibgrapi/2017/09.09.11.31
Last Update2017:09.09.11.31.11 (UTC) administrator
Metadata Repositorysid.inpe.br/sibgrapi/2017/09.09.11.31.11
Metadata Last Update2022:05.18.22.18.25 (UTC) administrator
Citation KeyMirandaJrThomGira:2017:GeDaAn
TitleGeometric Data Analysis Based on Manifold Learning with Applications for Image Understanding
FormatOn-line
Year2017
Access Date2024, May 02
Number of Files1
Size9442 KiB
2. Context
Author1 Miranda Junior, Gastao Florencio
2 Thomaz, Carlos Eduardo
3 Giraldi, Gilson Antonio
Affiliation1 Department of Mathematics, Federal University of Sergipe, Aracaju, Brazil
2 Department of Electrical Engineering, FEI, Sao Bernardo do Campo, Brazil
3 Department of Mathematics and Computational Methods, National Laboratory for Scientific Computing, Petropolis, Brazil
EditorTorchelsen, Rafael Piccin
Nascimento, Erickson Rangel do
Panozzo, Daniele
Liu, Zicheng
Farias, Mylène
Viera, Thales
Sacht, Leonardo
Ferreira, Nivan
Comba, João Luiz Dihl
Hirata, Nina
Schiavon Porto, Marcelo
Vital, Creto
Pagot, Christian Azambuja
Petronetto, Fabiano
Clua, Esteban
Cardeal, Flávio
e-Mail Addressgilson@lncc.br
Conference NameConference on Graphics, Patterns and Images, 30 (SIBGRAPI)
Conference LocationNiterói, RJ, Brazil
Date17-20 Oct. 2017
PublisherSociedade Brasileira de Computação
Publisher CityPorto Alegre
Book TitleProceedings
Tertiary TypeTutorial
History (UTC)2017-09-09 11:31:11 :: gilson@lncc.br -> administrator ::
2022-05-18 22:18:25 :: administrator -> :: 2017
3. Content and structure
Is the master or a copy?is the master
Content Stagecompleted
Transferable1
Keywordsmanifold learning
statistical learning
Riemannian manifolds
image analysis
deep learning
AbstractNowadays, 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.
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4. Conditions of access and use
data URLhttp://urlib.net/ibi/8JMKD3MGPAW/3PJRSSH
zipped data URLhttp://urlib.net/zip/8JMKD3MGPAW/3PJRSSH
Languageen
Target FilePID4980343.pdf
User Groupgilson@lncc.br
Visibilityshown
Update Permissionnot transferred
5. Allied materials
Mirror Repositorysid.inpe.br/banon/2001/03.30.15.38.24
Next Higher Units8JMKD3MGPAW/3PKCC58
Citing Item Listsid.inpe.br/sibgrapi/2017/09.12.13.04 10
sid.inpe.br/banon/2001/03.30.15.38.24 2
Host Collectionsid.inpe.br/banon/2001/03.30.15.38
6. Notes
Empty Fieldsarchivingpolicy archivist area callnumber contenttype copyholder copyright creatorhistory descriptionlevel dissemination doi edition electronicmailaddress group isbn issn label lineage mark nextedition notes numberofvolumes orcid organization pages parameterlist parentrepositories previousedition previouslowerunit progress project readergroup readpermission resumeid rightsholder schedulinginformation secondarydate secondarykey secondarymark secondarytype serieseditor session shorttitle sponsor subject tertiarymark type url versiontype volume


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