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Computing Persistent Homology [PDF]
Discrete and Computational Geometry, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Afra Zomorodian, Gunnar Carlsson
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Persistent homology classification algorithm [PDF]
PeerJ Computer Science, 2023 Data classification is an important aspect of machine learning, as it is utilized to solve issues in a wide variety of contexts. There are numerous classifiers, but there is no single best-performing classifier for all types of data, as the no free lunch
Mark Lexter D. De Lara
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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
Chengyuan Wu, Jie Wu
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Persistent homology of groups [PDF]
Journal of Group Theory, 2010 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.
Ellis, Graham, King, Simon A.
core +3 more sources
Going beyond persistent homology using persistent homology
Neural Information Processing Systems, 2023 Representational limits of message-passing graph neural networks (MP-GNNs), e.g., in terms of the Weisfeiler-Leman (WL) test for isomorphism, are well understood.
J. Immonen, Amauri H. Souza, Vikas Garg
semanticscholar +4 more sources
Persistent Homology and String Vacua [PDF]
Journal of High Energy Physics, 2015 We use methods from topological data analysis to study the topological features of certain distributions of string vacua. Topological data analysis is a multi-scale approach used to analyze the topological features of a dataset by identifying which ...
Cirafici, Michele
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Stratifying Multiparameter Persistent Homology [PDF]
SIAM Journal on Applied Algebra and Geometry, 2019 Minor improvements throughout. In particular: we extended the introduction, added Table 1, which gives a dictionary between terms used in PH and commutative algebra; we streamlined Section 3; we added Proposition 4.49 about the information captured by the cp-rank; we moved the code from the appendix to github.
Heather A Harrington +2 more
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Adaptive approximation of persistent homology
Journal of Applied and Computational Topology, 2023 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.
Maria Herick, M. Joachim, Jan Vahrenhold
semanticscholar +3 more sources
Automatic epileptic seizure detection based on persistent homology
Frontiers in Physiology, 2023 Epilepsy is a prevalent brain disease, which is quite difficult-to-treat or cure. This study developed a novel automatic seizure detection method based on the persistent homology method.
Ziyu Wang +7 more
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Stochastic convergence of persistence landscapes and silhouettes
Journal of Computational Geometry, 2015 Persistent homology is a widely used tool in Topological Data Analysis that encodes multi-scale topological information as a multiset of points in the plane called a persistence diagram.
Frédéric Chazal +4 more
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