Results 21 to 30 of about 1,043,448 (307)

Topological Regularization for Representation Learning via Persistent Homology

Mathematics, 2023
Generalization is challenging in small-sample-size regimes with over-parameterized deep neural networks, and a better representation is generally beneficial for generalization.
Muyi Chen, Daling Wang, Shi Feng, Yifei Zhang   +3 more
doaj   +2 more sources

Persistent Homology Combined with Machine Learning for Social Network Activity Analysis [PDF]

Entropy
Currently, the rapid development of social media enables people to communicate more and more frequently in the network. Classifying user activities in social networks helps to better understand user behavior in social networks.
Zhijian Zhang, Yuqing Sun, Yayun Liu, Lin Jiang, Zhengmi Li   +4 more
doaj   +2 more sources

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, Michael Joachim, Jan Vahrenhold   +2 more
semanticscholar   +3 more sources

Computing Persistent Homology [PDF]

Proceedings of the twentieth annual symposium on Computational geometry, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
A. Zomorodian, G. Carlsson
semanticscholar   +3 more sources

A review of some properties of persistent homology

Desimal, 2023
Every day, enormous complex geometric data are accumulating rapidly, and qualitative analysis is needed, which cannot be done properly without studying the shapes of those data.
Md. Safik Ullah, Mst. Sima Akhter Mou, Md. Morshed Bin Shiraj, Md. Mizanur Rahman, Md. Masum Murshed, Nasima Akhter   +5 more
doaj   +1 more source

Topology Applied to Machine Learning: From Global to Local

Frontiers in Artificial Intelligence, 2021
Through the use of examples, we explain one way in which applied topology has evolved since the birth of persistent homology in the early 2000s. The first applications of topology to data emphasized the global shape of a dataset, such as the three-circle
Henry Adams, Michael Moy
doaj   +1 more source

Selecting embedding delays: An overview of embedding techniques and a new method using persistent homology. [PDF]

Chaos, 2023
Delay embedding methods are a staple tool in the field of time series analysis and prediction. However, the selection of embedding parameters can have a big impact on the resulting analysis.
Eugene Tan, Shannon D. Algar, Débora C. Corrêa, Michael Small, T. Stemler, David M. Walker   +5 more
semanticscholar   +1 more source

Some Aspects of Persistent Homology Analysis on Phase Transition: Examples in an Effective QCD Model with Heavy Quarks

Universe, 2023
Recently, persistent homology analysis has been used to investigate phase structure. In this study, we apply persistent homology analysis to the QCD effective model with heavy quarks at finite imaginary chemical potential; i.e., the Potts model with the ...
Hayato Antoku, Kouji Kashiwa
doaj   +1 more source

Stable Vectorization of Multiparameter Persistent Homology using Signed Barcodes as Measures [PDF]

Neural Information Processing Systems, 2023
Persistent homology (PH) provides topological descriptors for geometric data, such as weighted graphs, which are interpretable, stable to perturbations, and invariant under, e.g., relabeling.
David Loiseaux, Luis Scoccola, Mathieu Carrière, M. B. Botnan, S. Oudot   +4 more
semanticscholar   +1 more source

Relative Persistent Homology

Discrete & Computational Geometry, 2022
AbstractThe alpha complex efficiently computes persistent homology of a point cloud $$X$$ X in Euclidean space when the dimension $$d$$ d is low. Given a subset $$A$$ A of $$X$$ X , relative Čech persistent homology
Nello Blaser, Morten Brun
openaire   +8 more sources