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In Topological Data Analysis, filtered chain complexes enter the persistence pipeline between the initial filtering of data and the final persistence invariants extraction. It is known that they admit a tame class of indecomposables, called interval
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c6bab4c2e19e5eab2785262387a97b57
https://hdl.handle.net/11380/1286365
https://hdl.handle.net/11380/1286365
Publikováno v:
Barbara Giunti
In this work, we provide a model structure on full subcategories of tame objects in functor categories indexed by continuous realizations of posets of dimension 1. We also characterize the indecomposable cofibrant objects when the landing category is
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Publikováno v:
Homology, Homotopy and Applications. 23:183-213
We set the foundations for a new approach to Topological Data Analysis (TDA) based on homotopical methods at chain complexes level. We present the category of tame parametrised chain complexes as a comprehensive environment that includes several case
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https://doi.org/10.4310/hha.2021.v23.n2.a11
https://doi.org/10.4310/hha.2021.v23.n2.a11
We study the algorithmic complexity of computing persistent homology of a randomly chosen filtration. Specifically, we prove upper bounds for the average fill-up (number of non-zero entries) of the boundary matrix on Erd\"os-R\'enyi and Vietoris-Rips
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Autor:
Barbara Giunti
Publikováno v:
Barbara Giunti
We present a row reduction algorithm to compute the barcode decomposition of persistence modules. This algorithm dualises the standard persistence one and clarifies the symmetry between clear and compress optimisations.
Comment: 5 pages
Comment: 5 pages
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::62673e7927c4087fbcfa52ea5a3bb2f4