@InProceedings{MirandaJrThomGira:2017:GeDaAn,
author = "Miranda Junior, Gastao Florencio and Thomaz, Carlos Eduardo and
Giraldi, Gilson Antonio",
affiliation = "Department of Mathematics, Federal University of Sergipe, Aracaju,
Brazil and Department of Electrical Engineering, FEI, Sao Bernardo
do Campo, Brazil and Department of Mathematics and Computational
Methods, National Laboratory for Scientific Computing, Petropolis,
Brazil",
title = "Geometric Data Analysis Based on Manifold Learning with
Applications for Image Understanding",
booktitle = "Proceedings...",
year = "2017",
editor = "Torchelsen, Rafael Piccin and Nascimento, Erickson Rangel do and
Panozzo, Daniele and Liu, Zicheng and Farias, Myl{\`e}ne and
Viera, Thales and Sacht, Leonardo and Ferreira, Nivan and Comba,
Jo{\~a}o Luiz Dihl and Hirata, Nina and Schiavon Porto, Marcelo
and Vital, Creto and Pagot, Christian Azambuja and Petronetto,
Fabiano and Clua, Esteban and Cardeal, Fl{\'a}vio",
organization = "Conference on Graphics, Patterns and Images, 30. (SIBGRAPI)",
publisher = "Sociedade Brasileira de Computa{\c{c}}{\~a}o",
address = "Porto Alegre",
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.",
conference-location = "Niter{\'o}i, RJ, Brazil",
conference-year = "17-20 Oct. 2017",
language = "en",
ibi = "8JMKD3MGPAW/3PJRSSH",
url = "http://urlib.net/ibi/8JMKD3MGPAW/3PJRSSH",
targetfile = "PID4980343.pdf",
urlaccessdate = "2024, May 02"
}