Results 51 to 60 of about 1,043,448 (307)
Sparse Nerves in Practice [PDF]
, 2019 Topological data analysis combines machine learning with methods from algebraic topology. Persistent homology, a method to characterize topological features occurring in data at multiple scales is of particular interest.
Aruni Choudhary +7 more
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Cosmology with persistent homology: a Fisher forecast [PDF]
Journal of Cosmology and Astroparticle PhysicsPersistent homology naturally addresses the multi-scale topological characteristics of the large-scale structure as a distribution of clusters, loops, and voids.
Jacky H. T. Yip +4 more
semanticscholar +1 more source
On the effectiveness of persistent homology [PDF]
Neural Information Processing Systems, 2022 Persistent homology (PH) is one of the most popular methods in Topological Data Analysis. Even though PH has been used in many different types of applications, the reasons behind its success remain elusive; in particular, it is not known for which ...
Renata Turkevs +2 more
semanticscholar +1 more source
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, Baris Coskunuzer
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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
doaj +1 more source
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.
Harrington, H +3 more
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Persistent hyperdigraph homology and persistent hyperdigraph Laplacians
Foundations of Data Science, 2023 Hypergraphs are useful mathematical models for describing complex relationships among members of a structured graph, while hyperdigraphs serve as a generalization that can encode asymmetric relationships in the data. However, obtaining topological information directly from hyperdigraphs remains a challenge.
Chen, Dong +3 more
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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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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 +1 more source
Persistent homology for 3D reconstruction evaluation [PDF]
, 2012 Space or voxel carving is a non-invasive technique that is used to produce a 3D volume and can be used in particular for the reconstruction of a 3D human model from images captured from a set of cameras placed around the subject.
Gutierrez, Antonio +3 more
core +2 more sources