Results 21 to 30 of about 714,887 (284)
Going beyond persistent homology using persistent homology
Advances in Neural Information Processing Systems 36, 2023 Accepted to NeurIPS ...
Immonen, Johanna Emilia +2 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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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 for 3D reconstruction evaluation [PDF]
, 2012 Space or voxel carving is a non-invasive technique that is used to produce a 3D volume and can be used in particular for the reconstruction of a 3D human model from images captured from a set of cameras placed around the subject.
Monaghan, David S. +10 more
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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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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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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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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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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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Persistent Homology of Semialgebraic Sets
SIAM Journal on Applied Algebra and Geometry, 2023 We give an algorithm with singly exponential complexity for computing the barcodes up to dimension $\ell$ (for any fixed $\ell \geq 0$) of the filtration of a given semi-algebraic set by the sub-level sets of a given polynomial. Our algorithm is the first algorithm for this problem with singly exponential complexity, and generalizes the corresponding ...
Saugata Basu, Negin Karisani
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