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Noise robustness of persistent homology on greyscale images, across filtrations and signatures

Topological data analysis is a recent and fast growing field that approaches the analysis of datasets using techniques from (algebraic) topology. Its main tool, persistent homology (PH), has seen a notable increase in applications in the last decade. Often cited as the most favourable property of PH...

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Detalles Bibliográficos
Autores principales: Turkeš, Renata, Nys, Jannes, Verdonck, Tim, Latré, Steven
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8462731/
https://www.ncbi.nlm.nih.gov/pubmed/34559812
http://dx.doi.org/10.1371/journal.pone.0257215
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author Turkeš, Renata
Nys, Jannes
Verdonck, Tim
Latré, Steven
author_facet Turkeš, Renata
Nys, Jannes
Verdonck, Tim
Latré, Steven
author_sort Turkeš, Renata
collection PubMed
description Topological data analysis is a recent and fast growing field that approaches the analysis of datasets using techniques from (algebraic) topology. Its main tool, persistent homology (PH), has seen a notable increase in applications in the last decade. Often cited as the most favourable property of PH and the main reason for practical success are the stability theorems that give theoretical results about noise robustness, since real data is typically contaminated with noise or measurement errors. However, little attention has been paid to what these stability theorems mean in practice. To gain some insight into this question, we evaluate the noise robustness of PH on the MNIST dataset of greyscale images. More precisely, we investigate to what extent PH changes under typical forms of image noise, and quantify the loss of performance in classifying the MNIST handwritten digits when noise is added to the data. The results show that the sensitivity to noise of PH is influenced by the choice of filtrations and persistence signatures (respectively the input and output of PH), and in particular, that PH features are often not robust to noise in a classification task.
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spelling pubmed-84627312021-09-25 Noise robustness of persistent homology on greyscale images, across filtrations and signatures Turkeš, Renata Nys, Jannes Verdonck, Tim Latré, Steven PLoS One Research Article Topological data analysis is a recent and fast growing field that approaches the analysis of datasets using techniques from (algebraic) topology. Its main tool, persistent homology (PH), has seen a notable increase in applications in the last decade. Often cited as the most favourable property of PH and the main reason for practical success are the stability theorems that give theoretical results about noise robustness, since real data is typically contaminated with noise or measurement errors. However, little attention has been paid to what these stability theorems mean in practice. To gain some insight into this question, we evaluate the noise robustness of PH on the MNIST dataset of greyscale images. More precisely, we investigate to what extent PH changes under typical forms of image noise, and quantify the loss of performance in classifying the MNIST handwritten digits when noise is added to the data. The results show that the sensitivity to noise of PH is influenced by the choice of filtrations and persistence signatures (respectively the input and output of PH), and in particular, that PH features are often not robust to noise in a classification task. Public Library of Science 2021-09-24 /pmc/articles/PMC8462731/ /pubmed/34559812 http://dx.doi.org/10.1371/journal.pone.0257215 Text en © 2021 Turkeš et al https://creativecommons.org/licenses/by/4.0/This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
spellingShingle Research Article
Turkeš, Renata
Nys, Jannes
Verdonck, Tim
Latré, Steven
Noise robustness of persistent homology on greyscale images, across filtrations and signatures
title Noise robustness of persistent homology on greyscale images, across filtrations and signatures
title_full Noise robustness of persistent homology on greyscale images, across filtrations and signatures
title_fullStr Noise robustness of persistent homology on greyscale images, across filtrations and signatures
title_full_unstemmed Noise robustness of persistent homology on greyscale images, across filtrations and signatures
title_short Noise robustness of persistent homology on greyscale images, across filtrations and signatures
title_sort noise robustness of persistent homology on greyscale images, across filtrations and signatures
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8462731/
https://www.ncbi.nlm.nih.gov/pubmed/34559812
http://dx.doi.org/10.1371/journal.pone.0257215
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