Results 21 to 30 of about 52,327 (248)
Discrete & Computational Geometry, 2022 AbstractThe alpha complex efficiently computes persistent homology of a point cloud $$X$$ X in Euclidean space when the dimension $$d$$ d is low. Given a subset $$A$$ A of $$X$$ X , relative Čech persistent homology
Nello Blaser, Morten Brun
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Flow estimation solely from image data through persistent homology analysis
Scientific Reports, 2021 Topological data analysis is an emerging concept of data analysis for characterizing shapes. A state-of-the-art tool in topological data analysis is persistent homology, which is expected to summarize quantified topological and geometric features ...
Anna Suzuki +6 more
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Persistent homology in graph power filtrations [PDF]
Royal Society Open Science, 2016 The persistence of homological features in simplicial complex representations of big datasets in Rn resulting from Vietoris–Rips or Čech filtrations is commonly used to probe the topological structure of such datasets.
Allen D. Parks, David J. Marchette
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Categorification of Persistent Homology [PDF]
Discrete & Computational Geometry, 2014 27 pages, v3: minor changes, to appear in Discrete & Computational ...
Peter Bubenik, Jonathan A. Scott
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Homological Algebra for Persistence Modules [PDF]
Foundations of Computational Mathematics, 2021 41 pages, accepted by Foundations of Computational ...
Peter Bubenik, Nikola Milicevic
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Persistent homology of groups [PDF]
Journal of Group Theory, 2011 We introduce and investigate notions of persistent homology for p-groups and for coclass trees of p-groups. Using computer techniques we show that persistent homology provides fairly strong homological invariants for p-groups of order at most 81. The strength of these invariants, and some elementary theoretical properties, suggest that persistent ...
Ellis, Graham, King, Simon
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Modeling of persistent homology [PDF]
Communications in Statistics - Theory and Methods, 2019 Topological Data Analysis (TDA) is a novel statistical technique, particularly powerful for the analysis of large and high dimensional data sets. Much of TDA is based on the tool of persistent homology, represented visually via persistence diagrams.
Agami, Sarit, Adler, Robert J.
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Geometric Approaches to Persistent Homology
SIAM Journal on Applied Algebra and Geometry, 2022 We introduce several geometric notions, including the width of a homology class, to the theory of persistent homology. These ideas provide geometric interpretations of persistence diagrams. Indeed, we give quantitative and geometric descriptions of the "life span" or "persistence" of a homology class. As a case study, we analyze the power filtration on
Henry Adams, Baris Coskunuzer
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Photonic band structure design using persistent homology
APL Photonics, 2021 The machine learning technique of persistent homology classifies complex systems or datasets by computing their topological features over a range of characteristic scales. There is growing interest in applying persistent homology to characterize physical
Daniel Leykam, Dimitris G. Angelakis
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Weighted persistent homology [PDF]
Involve, a Journal of Mathematics, 2019 We introduce weighted versions of the classical Čech and Vietoris-Rips complexes. We show that a version of the Vietoris-Rips Lemma holds for these weighted complexes and that they enjoy appropriate stability properties. We also give some preliminary applications of these weighted complexes.
Bell, Gregory +4 more
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