Homological scaffold via minimal homology bases

Abstract The homological scaffold leverages persistent homology to construct a topologically sound summary of a weighted network. However, its crucial dependency on the choice of representative cycles hinders the ability to trace back global features onto individual network components, unless one pr...

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Autores principales:	Marco Guerra, Alessandro De Gregorio, Ulderico Fugacci, Giovanni Petri, Francesco Vaccarino
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/22a7896fd70b47a09497c2280f34410c
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spelling	oai:doaj.org-article:22a7896fd70b47a09497c2280f34410c2021-12-02T15:54:01ZHomological scaffold via minimal homology bases10.1038/s41598-021-84486-12045-2322https://doaj.org/article/22a7896fd70b47a09497c2280f34410c2021-03-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-84486-1https://doaj.org/toc/2045-2322Abstract The homological scaffold leverages persistent homology to construct a topologically sound summary of a weighted network. However, its crucial dependency on the choice of representative cycles hinders the ability to trace back global features onto individual network components, unless one provides a principled way to make such a choice. In this paper, we apply recent advances in the computation of minimal homology bases to introduce a quasi-canonical version of the scaffold, called minimal, and employ it to analyze data both real and in silico. At the same time, we verify that, statistically, the standard scaffold is a good proxy of the minimal one for sufficiently complex networks.Marco GuerraAlessandro De GregorioUlderico FugacciGiovanni PetriFrancesco VaccarinoNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-17 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Marco Guerra Alessandro De Gregorio Ulderico Fugacci Giovanni Petri Francesco Vaccarino Homological scaffold via minimal homology bases
description	Abstract The homological scaffold leverages persistent homology to construct a topologically sound summary of a weighted network. However, its crucial dependency on the choice of representative cycles hinders the ability to trace back global features onto individual network components, unless one provides a principled way to make such a choice. In this paper, we apply recent advances in the computation of minimal homology bases to introduce a quasi-canonical version of the scaffold, called minimal, and employ it to analyze data both real and in silico. At the same time, we verify that, statistically, the standard scaffold is a good proxy of the minimal one for sufficiently complex networks.
format	article
author	Marco Guerra Alessandro De Gregorio Ulderico Fugacci Giovanni Petri Francesco Vaccarino
author_facet	Marco Guerra Alessandro De Gregorio Ulderico Fugacci Giovanni Petri Francesco Vaccarino
author_sort	Marco Guerra
title	Homological scaffold via minimal homology bases
title_short	Homological scaffold via minimal homology bases
title_full	Homological scaffold via minimal homology bases
title_fullStr	Homological scaffold via minimal homology bases
title_full_unstemmed	Homological scaffold via minimal homology bases
title_sort	homological scaffold via minimal homology bases
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/22a7896fd70b47a09497c2280f34410c
work_keys_str_mv	AT marcoguerra homologicalscaffoldviaminimalhomologybases AT alessandrodegregorio homologicalscaffoldviaminimalhomologybases AT uldericofugacci homologicalscaffoldviaminimalhomologybases AT giovannipetri homologicalscaffoldviaminimalhomologybases AT francescovaccarino homologicalscaffoldviaminimalhomologybases
_version_	1718385438025056256

Homological scaffold via minimal homology bases

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