Results 31 to 40 of about 52,327 (248)
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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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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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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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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Nori Diagrams and Persistent Homology [PDF]
Mathematics in Computer Science, 2019 45 ...
Yuri I. Manin, Matilde Marcolli
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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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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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Formation of Machine Learning Features Based on the Construction of Tropical Functions
Моделирование и анализ информационных систем, 2022 One of the main methods of computational topology and topological data analysis is persistent homology, which combines geometric and topological information about an object using persistent diagrams and barcodes.
Sergey N. Chukanov, Ilya S. Chukanov
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Persistent Homology applied to location problems
MATEC Web of Conferences, 2018 Different approaches to solve location problems in transport and logistics have been developed in the literature. This article introduces a new approach using the concept of persistent homology which has been proved to be an efficient method in ...
Bennis Driss, Gharib Fouad, Lebbar Ghita
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Analysis of Dynamic Evolution of Complex Brain Networks Based on Persistent Homology
Chinese Journal of Magnetic Resonance, 2021 Some studies have shown that the cognitive state in Alzheimer's disease (AD) patients is related to the changes of the temporal characteristics of dynamic functional connection. Persistent homology index analysis method provides a deeper insight into the
JIA Jia-ying +3 more
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