LOCA: LOcal Conformal Autoencoder for standardized data coordinates
| Autor: | Ioannis G. Kevrekidis, Erez Peterfreund, Felix Dietrich, Matan Gavish, Ofir Lindenbaum, Tom Bertalan, Ronald R. Coifman |
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| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
FOS: Computer and information sciences
Data Analysis Computer Science - Machine Learning Computer science Conformal map Machine Learning (stat.ML) 02 engineering and technology 01 natural sciences Machine Learning (cs.LG) Statistics - Machine Learning manifold learning 0103 physical sciences 0202 electrical engineering electronic engineering information engineering Invariant (mathematics) 010303 astronomy & astrophysics dimensionality reduction autoencoder Multidisciplinary Dimensionality reduction Applied Mathematics Canonical coordinates Nonlinear dimensionality reduction 020206 networking & telecommunications Riemannian manifold Reference Standards Autoencoder Physical Sciences Embedding Algorithm Algorithms canonical coordinates |
| Zdroj: | Proceedings of the National Academy of Sciences of the United States of America |
| Popis: | Significance A fundamental issue in empirical science is the ability to calibrate between different types of measurements/observations of the same phenomenon. This naturally suggests the selection of canonical variables, in the spirit of principal components, to enable matching/calibration among different observation modalities/instruments. We develop a method for extracting standardized, nonlinear, intrinsic coordinates from measured data, leading to a generalized isometric embedding of the observations. This is achieved through a local burst data acquisition strategy that allows us to capture the local z-scored structure. We implement this method using a local conformal autoencoder architecture and illustrate it computationally. The proposed embedding is fast, parallelizable, easy to implement using existing open-source neural network implementations and exhibits surprising interpolation and extrapolation capabilities. 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 Rd 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. |
| Databáze: | OpenAIRE |
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