Local conformal autoencoder for standardized data coordinates

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


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 languageAmerican English
Pages (from-to)30918-30927
Number of pages10
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number49
StatePublished - 8 Dec 2020

Bibliographical note

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


  • Autoencoder
  • Canonical coordinates
  • Dimensionality reduction
  • Manifold learning


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