Results 41 to 50 of about 1,143,028 (268)
Generalized Morse theory of distance functions to surfaces for persistent homology [PDF]
Advances in Applied Mathematics, 2023 This paper brings together three distinct theories with the goal of quantifying shape textures with complex morphologies. Distance fields are central objects in shape representation, while topological data analysis uses algebraic topology to characterize
Anna Song, K. Yim, Anthea Monod
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Categorification of Persistent Homology [PDF]
Discrete & Computational Geometry, 2014 27 pages, v3: minor changes, to appear in Discrete & Computational ...
Bubenik, Peter, Scott, Jonathan A.
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Topological data analysis for geographical information science using persistent homology
International Journal of Geographical Information Science, 2023 Topological data analysis (TDA) is an emerging field of research, which considers the application of topology to data analysis. Recently, these methods have been successfully applied to research problems in the field of geographical information science ...
P. Corcoran, Christopher B. Jones
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Filtered Feature Selection Algorithm Based on Persistent Homology [PDF]
Jisuanji kexue, 2023 The existing filtering feature selection algorithm ignores the correlation between features.This paper proposes a new filtering feature selection algorithm —the feature selection algorithm based on persistent homology(Rel-Betti algorithm),which can ...
YIN Xingzi, PENG Ningning, ZHAN Xueyan
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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
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Formation of Machine Learning Features Based on the Construction of Tropical Functions
Моделирование и анализ информационных систем, 2022 One of the main methods of computational topology and topological data analysis is persistent homology, which combines geometric and topological information about an object using persistent diagrams and barcodes.
Sergey N. Chukanov, Ilya S. Chukanov
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Multidimensional persistent homology is stable [PDF]
, 2009 Multidimensional persistence studies topological features of shapes by analyzing the lower level sets of vector-valued functions. The rank invariant completely determines the multidimensional analogue of persistent homology groups.
Cerri, Andrea +4 more
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bioRxiv, 2023 We present a topological method for the detection and quantification of bone microstructure from non-linear microscopy images. Specifically, we analyse second harmonic generation (SHG) and two photon excited autofluorescence (TPaF) images of bone tissue ...
Ysanne Pritchard +5 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 for MCI classification: a comparative analysis between graph and Vietoris-Rips filtrations [PDF]
Frontiers in NeuroscienceIntroduction Mild cognitive impairment (MCI), often linked to early neurodegeneration, is associated with subtle disruptions in brain connectivity.
Debanjali Bhattacharya +4 more
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