Results 11 to 20 of about 1,143,028 (268)
Distributed computation of persistent homology [PDF]
, 2013 Persistent homology is a popular and powerful tool for capturing topological features of data. Advances in algorithms for computing persistent homology have reduced the computation time drastically -- as long as the algorithm does not exhaust the ...
Bauer, Ulrich +2 more
core +3 more sources
Dualities in persistent (co)homology
Inverse Problems, 2010 We consider sequences of absolute and relative homology and cohomology groups that arise naturally for a filtered cell complex. We establish algebraic relationships between their persistence modules, and show that they contain equivalent information.
Chazal F +7 more
core +7 more sources
Topological Signals of Singularities in Ricci Flow [PDF]
Axioms, 2017 We implement methods from computational homology to obtain a topological signal of singularity formation in a selection of geometries evolved numerically by Ricci flow.
Paul M. Alsing +6 more
doaj +5 more sources
Geometric Approaches to Persistent Homology
SIAM Journal on Applied Algebra and Geometry, 2022 We introduce several geometric notions, including the width of a homology class, to the theory of persistent homology. These ideas provide geometric interpretations of persistence diagrams. Indeed, we give quantitative and geometric descriptions of the "life span" or "persistence" of a homology class. As a case study, we analyze the power filtration on
Henry Adams
exaly +4 more sources
Computing Persistent Homology of Directed Flag Complexes
Algorithms, 2020 We present a new computing package Flagser, designed to construct the directed flag complex of a finite directed graph, and compute persistent homology for flexibly defined filtrations on the graph and the resulting complex.
Daniel Lütgehetmann +3 more
doaj +3 more sources
Fast computation of persistent homology representatives with involuted persistent homology
Foundations of Data Science, 2023 Persistent homology is typically computed through persistent cohomology. While this generally improves the running time significantly, it does not facilitate extraction of homology representatives. The mentioned representatives are geometric manifestations of the corresponding holes and often carry desirable information.
Čufar, Matija, Virk, Žiga
exaly +4 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 +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
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
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 +5 more
semanticscholar +1 more source