A Probabilistic Result on Impulsive Noise Reduction in Topological Data Analysis through Group Equivariant Non-Expansive Operators

In recent years, group equivariant non-expansive operators (GENEOs) have started to find applications in the fields of Topological Data Analysis and Machine Learning. In this paper we show how these operators can be of use also for the removal of impulsive noise and to increase the stability of TDA...

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Detalles Bibliográficos
Autores principales: Frosini, Patrizio, Gridelli, Ivan, Pascucci, Andrea
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2023
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10453830/
https://www.ncbi.nlm.nih.gov/pubmed/37628180
http://dx.doi.org/10.3390/e25081150
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author Frosini, Patrizio
Gridelli, Ivan
Pascucci, Andrea
author_facet Frosini, Patrizio
Gridelli, Ivan
Pascucci, Andrea
author_sort Frosini, Patrizio
collection PubMed
description In recent years, group equivariant non-expansive operators (GENEOs) have started to find applications in the fields of Topological Data Analysis and Machine Learning. In this paper we show how these operators can be of use also for the removal of impulsive noise and to increase the stability of TDA in the presence of noisy data. In particular, we prove that GENEOs can control the expected value of the perturbation of persistence diagrams caused by uniformly distributed impulsive noise, when data are represented by L-Lipschitz functions from [Formula: see text] to [Formula: see text].
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spelling pubmed-104538302023-08-26 A Probabilistic Result on Impulsive Noise Reduction in Topological Data Analysis through Group Equivariant Non-Expansive Operators Frosini, Patrizio Gridelli, Ivan Pascucci, Andrea Entropy (Basel) Article In recent years, group equivariant non-expansive operators (GENEOs) have started to find applications in the fields of Topological Data Analysis and Machine Learning. In this paper we show how these operators can be of use also for the removal of impulsive noise and to increase the stability of TDA in the presence of noisy data. In particular, we prove that GENEOs can control the expected value of the perturbation of persistence diagrams caused by uniformly distributed impulsive noise, when data are represented by L-Lipschitz functions from [Formula: see text] to [Formula: see text]. MDPI 2023-07-31 /pmc/articles/PMC10453830/ /pubmed/37628180 http://dx.doi.org/10.3390/e25081150 Text en © 2023 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Frosini, Patrizio
Gridelli, Ivan
Pascucci, Andrea
A Probabilistic Result on Impulsive Noise Reduction in Topological Data Analysis through Group Equivariant Non-Expansive Operators
title A Probabilistic Result on Impulsive Noise Reduction in Topological Data Analysis through Group Equivariant Non-Expansive Operators
title_full A Probabilistic Result on Impulsive Noise Reduction in Topological Data Analysis through Group Equivariant Non-Expansive Operators
title_fullStr A Probabilistic Result on Impulsive Noise Reduction in Topological Data Analysis through Group Equivariant Non-Expansive Operators
title_full_unstemmed A Probabilistic Result on Impulsive Noise Reduction in Topological Data Analysis through Group Equivariant Non-Expansive Operators
title_short A Probabilistic Result on Impulsive Noise Reduction in Topological Data Analysis through Group Equivariant Non-Expansive Operators
title_sort probabilistic result on impulsive noise reduction in topological data analysis through group equivariant non-expansive operators
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10453830/
https://www.ncbi.nlm.nih.gov/pubmed/37628180
http://dx.doi.org/10.3390/e25081150
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