Results 31 to 40 of about 714,887 (284)
Weighted persistent homology [PDF]
Rocky Mountain Journal of Mathematics, 2018 In this paper we develop the theory of weighted persistent homology. In 1990, Robert J. Dawson was the first to study in depth the homology of weighted simplicial complexes. We generalize the definitions of weighted simplicial complex and the homology of weighted simplicial complex to allow weights in an integral domain $R$. Then we study the resulting
Ren, Shiquan, Wu, Chengyuan, Wu, Jie
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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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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
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The Persistent Homology of a Self-Map [PDF]
Foundations of Computational Mathematics, 2014 The main result in this paper is the construction of an algorithm that takes a simplicial self map of a topological space and derives a persistent homology associated to the self map. The persistent homology is obtained as a tower of eigenspaces given by the homology of the chain maps induced by the self map.
Herbert Edelsbrunner +2 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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Representability of algebraic topology for biomolecules in machine learning based scoring and virtual screening. [PDF]
PLoS Computational Biology, 2018 This work introduces a number of algebraic topology approaches, including multi-component persistent homology, multi-level persistent homology, and electrostatic persistence for the representation, characterization, and description of small molecules and
Zixuan Cang, Lin Mu, Guo-Wei Wei
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Object-oriented persistent homology [PDF]
Journal of Computational Physics, 2016 Persistent homology provides a new approach for the topological simplification of big data via measuring the life time of intrinsic topological features in a filtration process and has found its success in scientific and engineering applications. However, such a success is essentially limited to qualitative data classification and analysis.
Bao Wang 0001, Guo-Wei Wei 0001
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Magnitude meets persistence. Homology theories for filtered simplicial sets [PDF]
, 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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Promises and pitfalls of topological data analysis for brain connectivity analysis
NeuroImage, 2021 Developing sensitive and reliable methods to distinguish normal and abnormal brain states is a key neuroscientific challenge. Topological Data Analysis, despite its relative novelty, already generated many promising applications, including in ...
Luigi Caputi +2 more
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Filtered Feature Selection Algorithm Based on Persistent Homology [PDF]
Jisuanji kexue, 2023 The existing filtering feature selection algorithm ignores the correlation between features.This paper proposes a new filtering feature selection algorithm —the feature selection algorithm based on persistent homology(Rel-Betti algorithm),which can ...
YIN Xingzi, PENG Ningning, ZHAN Xueyan
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