Results 21 to 30 of about 54,259 (246)
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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Relative Persistent Homology [PDF]
, 2020 The alpha complex efficiently computes persistent homology of a point cloud X in Euclidean space when the dimension d is low. Given a subset A of X, relative persistent homology can be computed as the persistent homology of the relative Čech complex Č(X,
Brun, Morten, Blaser, Nello
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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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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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Machine learning explainability through persistent homology [PDF]
, 2023 openIl nostro obiettivo è acquisire informazioni sulla dinamica di apprendimento delle reti neurali utilizzando uno degli strumenti principali della Topological Data Analysis: l'omologia persistente.
GRIDELLI, IVAN
core
Adaptive Approximation of Persistent Homology
Journal of Applied and Computational Topology, 2023 Abstract We study an important preprocessing step for the efficient calculation of persistent homology: coarsening a set of points while controlling the quality of the induced persistence diagram. This coarsening step is instrumental in reducing the overall runtime of state-of-the-art algorithms such as Ripser, GUDHI, or PHAT.
Maria Herick +2 more
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Nori Diagrams and Persistent Homology [PDF]
Mathematics in Computer Science, 2019 45 ...
Yuri I. Manin, Matilde Marcolli
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The Persistent Homology of Cyclic Graphs
International Journal of Computational Geometry & Applications, 2022 We give an [Formula: see text] algorithm for computing the [Formula: see text]-dimensional persistent homology of a filtration of clique complexes of cyclic graphs on [Formula: see text] vertices. This is nearly quadratic in the number of vertices [Formula: see text], and therefore a large improvement upon the traditional persistent homology algorithm,
Henry Adams +2 more
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On the Structural Theorem of Persistent Homology [PDF]
Discrete & Computational Geometry, 2018 We study the categorical framework for the computation of persistent homology, without reliance on a particular computational algorithm. The computation of persistent homology is commonly summarized as a matrix theorem, which we call the Matrix Structural Theorem.
Killian Meehan +2 more
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Magnitude meets persistence. Homology theories for filtered simplicial sets
, 2021 The Euler characteristic is an invariant of a topological space that in a precise sense captures its canonical notion of size, akin to the cardinality of a set.
Otter, Nina, Otter, N
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