Results 41 to 50 of about 52,327 (248)
On the Structural Theorem of Persistent Homology [PDF]
Discrete & Computational Geometry, 2018 We study the categorical framework for the computation of persistent homology, without reliance on a particular computational algorithm. The computation of persistent homology is commonly summarized as a matrix theorem, which we call the Matrix Structural Theorem.
Killian Meehan +2 more
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Model comparison via simplicial complexes and persistent homology
Royal Society Open Science, 2021 In many scientific and technological contexts, we have only a poor understanding of the structure and details of appropriate mathematical models. We often, therefore, need to compare different models.
Sean T. Vittadello, Michael P. H. Stumpf
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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 available memory.
Ulrich Bauer +2 more
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Topological data analysis for the string landscape
Journal of High Energy Physics, 2019 Persistent homology computes the multiscale topology of a data set by using a sequence of discrete complexes. In this paper, we propose that persistent homology may be a useful tool for studying the structure of the landscape of string vacua. As a scaled-
Alex Cole, Gary Shiu
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Stable volumes for persistent homology
Journal of Applied and Computational Topology, 2023 AbstractThis paper proposes a stable volume and a stable volume variant, referred to as a stable sub-volume, for more reliable data analysis using persistent homology. In prior research, an optimal cycle and similar ideas have been proposed to identify the homological structure corresponding to each birth-death pair in a persistence diagram. While this
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A Bayesian Framework for Persistent Homology
SIAM Journal on Mathematics of Data Science, 2020 Persistence diagrams offer a way to summarize topological and geometric properties latent in datasets. While several methods have been developed that utilize persistence diagrams in statistical inference, a full Bayesian treatment remains absent. This paper, relying on the theory of point processes, presents a Bayesian framework for inference with ...
Vasileios Maroulas +2 more
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The Comparison of Diffeomorphic Images Based on the Construction of Persistent Homology
Моделирование и анализ информационных систем, 2019 An object shape analysis is a problem that is related to such areas as geometry, topology, image processing and machine learning. For analyzing the form, the deformation between the source and terminal form of the object is estimated.
Sergey N. Chukanov
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The Persistent Homology of a Self-Map [PDF]
Foundations of Computational Mathematics, 2014 The main result in this paper is the construction of an algorithm that takes a simplicial self map of a topological space and derives a persistent homology associated to the self map. The persistent homology is obtained as a tower of eigenspaces given by the homology of the chain maps induced by the self map.
Herbert Edelsbrunner +2 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.
Bao Wang 0001, Guo-Wei Wei 0001
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Homological properties of persistent homology
Journal of Algebra and Its ApplicationsIn this paper, we investigate to what extent persistent homology benefits from the properties of a homology theory. We show that persistent homology benefits from a Mayer–Vietoris sequence and a long exact sequence for a pair if one works with graded persistence modules.
Hani̇fe Varlı +2 more
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