ToFU: topology functional units for deep learning

DOI10.3934/fods.2021021OpenAlexW3199826041MaRDI QIDQ6154235

David Boothe, Vasileios Maroulas, Piotr J. Franaszczuk, Christopher Oballe

Publication date: 14 February 2024

Published in: Foundations of Data Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/fods.2021021

zbMATH Keywords

neural networksmachine learningtopological data analysisactivation functionsdeep learningvariational autoencoders

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Persistent homology and applications, topological data analysis (55N31)

Cites Work

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• Confidence sets for persistence diagrams
• Fréchet means for distributions of persistence diagrams
• Linear model of brain electrical activity - EEG as a superposition of damped oscillatory modes
• Computational homology
• Signal classification with a point process distance on the space of persistence diagrams
• Computing persistent homology
• Functional summaries of persistence diagrams
• A stable cardinality distance for topological classification
• Modelling persistence diagrams with planar point processes, and revealing topology with bagplots
• The Gromov-Wasserstein distance: a brief overview
• Probabilistic Fréchet means for time varying persistence diagrams
• Efficient Computation of Persistent Homology for Cubical Data
• Probability measures on the space of persistence diagrams
• The Accumulated Persistence Function, a New Useful Functional Summary Statistic for Topological Data Analysis, With a View to Brain Artery Trees and Spatial Point Process Applications
• Topology and data
• Persistent homology transform for modeling shapes and surfaces
• Stochastic Convergence of Persistence Landscapes and Silhouettes
• Decomposition of pointwise finite-dimensional persistence modules
• A Bayesian Framework for Persistent Homology
• An Introduction to Variational Autoencoders
• Nonparametric Estimation of Probability Density Functions of Random Persistence Diagrams
• Tropical Sufficient Statistics for Persistent Homology
• Persistence Images: A Stable Vector Representation of Persistent Homology
• Understanding Machine Learning
• Statistical topological data analysis using persistence landscapes
• Barcodes: The persistent topology of data

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