Results 41 to 50 of about 1,043,448 (307)
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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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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Adaptive Topological Feature via Persistent Homology: Filtration Learning for Point Clouds [PDF]
Neural Information Processing Systems, 2023 Machine learning for point clouds has been attracting much attention, with many applications in various fields, such as shape recognition and material science.
Naoki Nishikawa +2 more
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Multidimensional persistent homology is stable [PDF]
, 2009 Multidimensional persistence studies topological features of shapes by analyzing the lower level sets of vector-valued functions. The rank invariant completely determines the multidimensional analogue of persistent homology groups.
Cerri, Andrea +4 more
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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.
Wang, Bao, Wei, Guo-Wei
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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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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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Topological data analysis for geographical information science using persistent homology
International Journal of Geographical Information Science, 2023 Topological data analysis (TDA) is an emerging field of research, which considers the application of topology to data analysis. Recently, these methods have been successfully applied to research problems in the field of geographical information science ...
P. Corcoran, Christopher B. Jones
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Probing Multipartite Entanglement Through Persistent Homology [PDF]
Communications in Mathematical Physics, 2023 We propose a study of multipartite entanglement through persistent homology, a tool used in topological data analysis. In persistent homology, a 1-parameter filtration of simplicial complexes called a persistence complex is used to reveal persistent ...
Greg A. Hamilton, Felix Leditzky
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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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