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Local conformal autoencoder for standardized data coordinates

We propose a local conformal autoencoder (LOCA) for standardized data coordinates. LOCA is a deep learning-based method for obtaining standardized data coordinates from scientific measurements. Data observations are modeled as samples from an unknown, nonlinear deformation of an underlying Riemannia...

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Autores principales: Peterfreund, Erez, Lindenbaum, Ofir, Dietrich, Felix, Bertalan, Tom, Gavish, Matan, Kevrekidis, Ioannis G., Coifman, Ronald R.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: National Academy of Sciences 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7733838/
https://www.ncbi.nlm.nih.gov/pubmed/33229581
http://dx.doi.org/10.1073/pnas.2014627117
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author Peterfreund, Erez
Lindenbaum, Ofir
Dietrich, Felix
Bertalan, Tom
Gavish, Matan
Kevrekidis, Ioannis G.
Coifman, Ronald R.
author_facet Peterfreund, Erez
Lindenbaum, Ofir
Dietrich, Felix
Bertalan, Tom
Gavish, Matan
Kevrekidis, Ioannis G.
Coifman, Ronald R.
author_sort Peterfreund, Erez
collection PubMed
description We propose a local conformal autoencoder (LOCA) for standardized data coordinates. LOCA is a deep learning-based method for obtaining standardized data coordinates from scientific measurements. Data observations are modeled as samples from an unknown, nonlinear deformation of an underlying Riemannian manifold, which is parametrized by a few normalized, latent variables. We assume a repeated measurement sampling strategy, common in scientific measurements, and present a method for learning an embedding in [Formula: see text] that is isometric to the latent variables of the manifold. The coordinates recovered by our method are invariant to diffeomorphisms of the manifold, making it possible to match between different instrumental observations of the same phenomenon. Our embedding is obtained using LOCA, which is an algorithm that learns to rectify deformations by using a local z-scoring procedure, while preserving relevant geometric information. We demonstrate the isometric embedding properties of LOCA in various model settings and observe that it exhibits promising interpolation and extrapolation capabilities, superior to the current state of the art. Finally, we demonstrate LOCA’s efficacy in single-site Wi-Fi localization data and for the reconstruction of three-dimensional curved surfaces from two-dimensional projections.
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spelling pubmed-77338382020-12-21 Local conformal autoencoder for standardized data coordinates Peterfreund, Erez Lindenbaum, Ofir Dietrich, Felix Bertalan, Tom Gavish, Matan Kevrekidis, Ioannis G. Coifman, Ronald R. Proc Natl Acad Sci U S A Physical Sciences We propose a local conformal autoencoder (LOCA) for standardized data coordinates. LOCA is a deep learning-based method for obtaining standardized data coordinates from scientific measurements. Data observations are modeled as samples from an unknown, nonlinear deformation of an underlying Riemannian manifold, which is parametrized by a few normalized, latent variables. We assume a repeated measurement sampling strategy, common in scientific measurements, and present a method for learning an embedding in [Formula: see text] that is isometric to the latent variables of the manifold. The coordinates recovered by our method are invariant to diffeomorphisms of the manifold, making it possible to match between different instrumental observations of the same phenomenon. Our embedding is obtained using LOCA, which is an algorithm that learns to rectify deformations by using a local z-scoring procedure, while preserving relevant geometric information. We demonstrate the isometric embedding properties of LOCA in various model settings and observe that it exhibits promising interpolation and extrapolation capabilities, superior to the current state of the art. Finally, we demonstrate LOCA’s efficacy in single-site Wi-Fi localization data and for the reconstruction of three-dimensional curved surfaces from two-dimensional projections. National Academy of Sciences 2020-12-08 2020-11-23 /pmc/articles/PMC7733838/ /pubmed/33229581 http://dx.doi.org/10.1073/pnas.2014627117 Text en Copyright © 2020 the Author(s). Published by PNAS. https://creativecommons.org/licenses/by-nc-nd/4.0/ https://creativecommons.org/licenses/by-nc-nd/4.0/This open access article is distributed under Creative Commons Attribution-NonCommercial-NoDerivatives License 4.0 (CC BY-NC-ND) (https://creativecommons.org/licenses/by-nc-nd/4.0/) .
spellingShingle Physical Sciences
Peterfreund, Erez
Lindenbaum, Ofir
Dietrich, Felix
Bertalan, Tom
Gavish, Matan
Kevrekidis, Ioannis G.
Coifman, Ronald R.
Local conformal autoencoder for standardized data coordinates
title Local conformal autoencoder for standardized data coordinates
title_full Local conformal autoencoder for standardized data coordinates
title_fullStr Local conformal autoencoder for standardized data coordinates
title_full_unstemmed Local conformal autoencoder for standardized data coordinates
title_short Local conformal autoencoder for standardized data coordinates
title_sort local conformal autoencoder for standardized data coordinates
topic Physical Sciences
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7733838/
https://www.ncbi.nlm.nih.gov/pubmed/33229581
http://dx.doi.org/10.1073/pnas.2014627117
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