On the Topological Data Analysis extensions and comparisons

On the Topological Data Analysis extensions and comparisons

Topological Data Analysis is an emerging field at the intersection of algebraic topology and statistical inference aimed at describing the shapes objects represented as point cloud data in the multidimensional space. Since the range of applications of shape analysis is enormous, new tests have given...

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Main Authors: H.N. Alaa, S.A. Mohamed
Format: Article
Language:English
Published: SpringerOpen 2017-10-01
Series:Journal of the Egyptian Mathematical Society
Online Access:http://www.sciencedirect.com/science/article/pii/S1110256X17300433
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spelling doaj-f721d004e595464e917c37b39c387e762020-11-25T02:01:55ZengSpringerOpenJournal of the Egyptian Mathematical Society1110-256X2017-10-01254406413On the Topological Data Analysis extensions and comparisonsH.N. Alaa0S.A. Mohamed1Corresponding author.; Department of Mathematics, Faculty of Science Aswan University, EgyptDepartment of Mathematics, Faculty of Science Aswan University, EgyptTopological Data Analysis is an emerging field at the intersection of algebraic topology and statistical inference aimed at describing the shapes objects represented as point cloud data in the multidimensional space. Since the range of applications of shape analysis is enormous, new tests have given birth to the field of TDA. In this habilitation study three TDA-oriented tests are discussed. A new test based on metric functions is proposed. A small simulation study among the preceding tests has been employed via Monte Carlo simulation. All the mentioned tests in the vignette are activated by real world data within educational field. MSC: 55N35, 55U05, 62H99, Keywords: Topology â homology-persistence landscape, Topological Data Analysis, Testing hypotheseshttp://www.sciencedirect.com/science/article/pii/S1110256X17300433
collection DOAJ
language English
format Article
sources DOAJ
author H.N. Alaa
S.A. Mohamed
spellingShingle H.N. Alaa
S.A. Mohamed
On the Topological Data Analysis extensions and comparisons
Journal of the Egyptian Mathematical Society
author_facet H.N. Alaa
S.A. Mohamed
author_sort H.N. Alaa
title On the Topological Data Analysis extensions and comparisons
title_short On the Topological Data Analysis extensions and comparisons
title_full On the Topological Data Analysis extensions and comparisons
title_fullStr On the Topological Data Analysis extensions and comparisons
title_full_unstemmed On the Topological Data Analysis extensions and comparisons
title_sort on the topological data analysis extensions and comparisons
publisher SpringerOpen
series Journal of the Egyptian Mathematical Society
issn 1110-256X
publishDate 2017-10-01
description Topological Data Analysis is an emerging field at the intersection of algebraic topology and statistical inference aimed at describing the shapes objects represented as point cloud data in the multidimensional space. Since the range of applications of shape analysis is enormous, new tests have given birth to the field of TDA. In this habilitation study three TDA-oriented tests are discussed. A new test based on metric functions is proposed. A small simulation study among the preceding tests has been employed via Monte Carlo simulation. All the mentioned tests in the vignette are activated by real world data within educational field. MSC: 55N35, 55U05, 62H99, Keywords: Topology â homology-persistence landscape, Topological Data Analysis, Testing hypotheses
url http://www.sciencedirect.com/science/article/pii/S1110256X17300433
work_keys_str_mv AT hnalaa onthetopologicaldataanalysisextensionsandcomparisons
AT samohamed onthetopologicaldataanalysisextensionsandcomparisons
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