Results 11 to 20 of about 714,887 (284)
Relative Persistent Homology [PDF]
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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Homology and persistent homology [PDF]
, 2020 Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Francisco Belchí ...
Nobbe Fisas, Fritz Pere
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Persistent Intersection Homology
Foundations of Computational Mathematics, 2010 Persistent homology uses a filtration on a topological space to define birth and death of a homology class. The \(r\)-dimensional classes that are born at stage \(i\) and die at stage \(j\) form the pair group \(P^{i,j}_r\), a vector space over the field with 2 elements, of the filtered space.
Paul Bendich, John Harer
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Introduction to Persistent Homology. [PDF]
, 2016 This video presents an introduction to persistent homology, aimed at a viewer who has mathematical aptitude but not necessarily knowledge of algebraic topology. Persistent homology is an algebraic method of discerning the topological features of complex data, which in recent years has found applications in fields such as image processing and biological
Wright, Matthew L.
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Homological properties of persistent homology
Journal of Algebra and Its ApplicationsIn this paper, we investigate to what extent persistent homology benefits from the properties of a homology theory. We show that persistent homology benefits from a Mayer–Vietoris sequence and a long exact sequence for a pair if one works with graded persistence modules.
Hani̇fe Varlı +2 more
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G-invariant persistent homology [PDF]
Mathematical Methods in the Applied Sciences, 2014 Classical persistent homology is not tailored to study the action of transformation groups different from the group Homeo(X) of all self-homeomorphisms of a topological space X. In order to obtain better lower bounds for the natural pseudo-distance d_G associated with a subgroup G of Homeo(X), we need to adapt persistent homology and consider G ...
Frosini, Patrizio, Patrizio Frosini
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On the Effectiveness of Persistent Homology
Advances in Neural Information Processing Systems 35, 2022 Persistent homology (PH) is one of the most popular methods in Topological Data Analysis. Even though PH has been used in many different types of applications, the reasons behind its success remain elusive; in particular, it is not known for which classes of problems it is most effective, or to what extent it can detect geometric or topological ...
Turkeš, Renata +2 more
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Topology Applied to Machine Learning: From Global to Local
Frontiers in Artificial Intelligence, 2021 Through the use of examples, we explain one way in which applied topology has evolved since the birth of persistent homology in the early 2000s. The first applications of topology to data emphasized the global shape of a dataset, such as the three-circle
Henry Adams, Michael Moy
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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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Universe, 2023 Recently, persistent homology analysis has been used to investigate phase structure. In this study, we apply persistent homology analysis to the QCD effective model with heavy quarks at finite imaginary chemical potential; i.e., the Potts model with the ...
Hayato Antoku, Kouji Kashiwa
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