Local conformal autoencoder for standardized data coordinates

Erez Peterfreund, Ofir Lindenbaum, Felix Dietrich, Tom Bertalan, Matan Gavish, Ioannis G. Kevrekidis, Ronald R. Coifman

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

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 ℝdthat 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.

Original languageEnglish
Pages (from-to)30918-30927
Number of pages10
JournalProceedings of the National Academy of Sciences of the United States of America
Volume117
Issue number49
DOIs
StatePublished - 8 Dec 2020
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2020 National Academy of Sciences. All rights reserved.

Funding

ACKNOWLEDGMENTS This work was partially supported by the Defense Advanced Research Projects Agency Physics of Artificial Intelligence program (Agreement HR00111890032, Dr. T. Senator). E.P. has been partially supported by the Blavatnik Interdisciplinary Research Center, the Feder-mann Research Center (Hebrew University), and Israeli Science Foundation research grant 1523/16. This work was partially supported by the Defense Advanced Research Projects Agency Physics of Artificial Intelligence program (Agreement HR00111890032, Dr. T. Senator). E.P. has been partially supported by the Blavatnik Interdisciplinary Research Center, the Federmann Research Center (Hebrew University), and Israeli Science Foundation research grant 1523/16.

FundersFunder number
Blavatnik Interdisciplinary Research Center
Feder-mann Research Center
Federmann Research Center
Israeli Science Foundation1523/16
National Institute of General Medical SciencesR01GM131642
National Institute of Neurological Disorders and StrokeR01NS100049
Defense Advanced Research Projects AgencyHR00111890032
Hebrew University of Jerusalem

    Keywords

    • Autoencoder
    • Canonical coordinates
    • Dimensionality reduction
    • Manifold learning

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