TY - JOUR
T1 - Local conformal autoencoder for standardized data coordinates
AU - Peterfreund, Erez
AU - Lindenbaum, Ofir
AU - Dietrich, Felix
AU - Bertalan, Tom
AU - Gavish, Matan
AU - Kevrekidis, Ioannis G.
AU - Coifman, Ronald R.
N1 - Publisher Copyright:
© 2020 National Academy of Sciences. All rights reserved.
PY - 2020/12/8
Y1 - 2020/12/8
N2 - 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.
AB - 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.
KW - Autoencoder
KW - Canonical coordinates
KW - Dimensionality reduction
KW - Manifold learning
UR - http://www.scopus.com/inward/record.url?scp=85097576702&partnerID=8YFLogxK
U2 - 10.1073/pnas.2014627117
DO - 10.1073/pnas.2014627117
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C2 - 33229581
AN - SCOPUS:85097576702
SN - 0027-8424
VL - 117
SP - 30918
EP - 30927
JO - Proceedings of the National Academy of Sciences of the United States of America
JF - Proceedings of the National Academy of Sciences of the United States of America
IS - 49
ER -