1. Identity statement | |
Reference Type | Conference Paper (Conference Proceedings) |
Site | sibgrapi.sid.inpe.br |
Holder Code | ibi 8JMKD3MGPEW34M/46T9EHH |
Identifier | 8JMKD3MGPAW/3PJRSSH |
Repository | sid.inpe.br/sibgrapi/2017/09.09.11.31 |
Last Update | 2017:09.09.11.31.11 (UTC) administrator |
Metadata Repository | sid.inpe.br/sibgrapi/2017/09.09.11.31.11 |
Metadata Last Update | 2022:05.18.22.18.25 (UTC) administrator |
Citation Key | MirandaJrThomGira:2017:GeDaAn |
Title | Geometric Data Analysis Based on Manifold Learning with Applications for Image Understanding |
Format | On-line |
Year | 2017 |
Access Date | 2024, Oct. 15 |
Number of Files | 1 |
Size | 9442 KiB |
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2. Context | |
Author | 1 Miranda Junior, Gastao Florencio 2 Thomaz, Carlos Eduardo 3 Giraldi, Gilson Antonio |
Affiliation | 1 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 |
Editor | Torchelsen, 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 Address | gilson@lncc.br |
Conference Name | Conference on Graphics, Patterns and Images, 30 (SIBGRAPI) |
Conference Location | Niterói, RJ, Brazil |
Date | 17-20 Oct. 2017 |
Publisher | Sociedade Brasileira de Computação |
Publisher City | Porto Alegre |
Book Title | Proceedings |
Tertiary Type | Tutorial |
History (UTC) | 2017-09-09 11:31:11 :: gilson@lncc.br -> administrator :: 2022-05-18 22:18:25 :: administrator -> :: 2017 |
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3. Content and structure | |
Is the master or a copy? | is the master |
Content Stage | completed |
Transferable | 1 |
Keywords | manifold learning statistical learning Riemannian manifolds image analysis deep learning |
Abstract | 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. |
Arrangement | urlib.net > SDLA > Fonds > SIBGRAPI 2017 > Geometric Data Analysis... |
doc Directory Content | access |
source Directory Content | there are no files |
agreement Directory Content | |
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4. Conditions of access and use | |
data URL | http://urlib.net/ibi/8JMKD3MGPAW/3PJRSSH |
zipped data URL | http://urlib.net/zip/8JMKD3MGPAW/3PJRSSH |
Language | en |
Target File | PID4980343.pdf |
User Group | gilson@lncc.br |
Visibility | shown |
Update Permission | not transferred |
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5. Allied materials | |
Mirror Repository | sid.inpe.br/banon/2001/03.30.15.38.24 |
Next Higher Units | 8JMKD3MGPAW/3PKCC58 |
Citing Item List | sid.inpe.br/sibgrapi/2017/09.12.13.04 45 sid.inpe.br/banon/2001/03.30.15.38.24 2 |
Host Collection | sid.inpe.br/banon/2001/03.30.15.38 |
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6. Notes | |
Empty Fields | archivingpolicy 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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