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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Autores principales:	Renata Turkeš, Jannes Nys, Tim Verdonck, Steven Latré
Formato:	article
Lenguaje:	EN
Publicado:	Public Library of Science (PLoS) 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/bf20c915b55b4b1882e644bda6954ef5
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id	oai:doaj.org-article:bf20c915b55b4b1882e644bda6954ef5
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spelling	oai:doaj.org-article:bf20c915b55b4b1882e644bda6954ef52021-12-02T20:06:09ZNoise robustness of persistent homology on greyscale images, across filtrations and signatures.1932-620310.1371/journal.pone.0257215https://doaj.org/article/bf20c915b55b4b1882e644bda6954ef52021-01-01T00:00:00Zhttps://doi.org/10.1371/journal.pone.0257215https://doaj.org/toc/1932-6203Topological 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.Renata TurkešJannes NysTim VerdonckSteven LatréPublic Library of Science (PLoS)articleMedicineRScienceQENPLoS ONE, Vol 16, Iss 9, p e0257215 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Renata Turkeš Jannes Nys Tim Verdonck Steven Latré Noise robustness of persistent homology on greyscale images, across filtrations and signatures.
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.
format	article
author	Renata Turkeš Jannes Nys Tim Verdonck Steven Latré
author_facet	Renata Turkeš Jannes Nys Tim Verdonck Steven Latré
author_sort	Renata Turkeš
title	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_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_sort	noise robustness of persistent homology on greyscale images, across filtrations and signatures.
publisher	Public Library of Science (PLoS)
publishDate	2021
url	https://doaj.org/article/bf20c915b55b4b1882e644bda6954ef5
work_keys_str_mv	AT renataturkes noiserobustnessofpersistenthomologyongreyscaleimagesacrossfiltrationsandsignatures AT jannesnys noiserobustnessofpersistenthomologyongreyscaleimagesacrossfiltrationsandsignatures AT timverdonck noiserobustnessofpersistenthomologyongreyscaleimagesacrossfiltrationsandsignatures AT stevenlatre noiserobustnessofpersistenthomologyongreyscaleimagesacrossfiltrationsandsignatures
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Noise robustness of persistent homology on greyscale images, across filtrations and signatures.

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