arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2004.07234cs.LGstat.ML
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LOCA: LOcal Conformal Autoencoder for standardized data coordinates

Johns Hopkins University(约翰斯·霍普金斯大学);Hebrew University of Jerusalem(耶路撒冷希伯来大学);Yale University(耶鲁大学)

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

英文摘要:

We propose a deep-learning based method for obtaining standardized data coordinates from scientific measurements.Data observations are modeled as samples from an unknown, non-linear deformation of an underlying Riemannian manifold, which is parametrized by a few normalized latent variables. By leveraging a repeated measurement sampling strategy, we present a method for learning an embedding in $\mathbb{R}^d$ that is isometric to the latent variables of the manifold. These data coordinates, being invariant under smooth changes of variables, enable matching between different instrumental observations of the same phenomenon. Our embedding is obtained using a LOcal Conformal Autoencoder (LOCA), an algorithm that constructs an embedding to rectify deformations by using a local z-scoring procedure while preserving relevant geometric information. We demonstrate the isometric embedding properties of LOCA on various model settings and observe that it exhibits promising interpolation and extrapolation capabilities. Finally, we apply LOCA to single-site Wi-Fi localization data, and to $3$-dimensional curved surface estimation based on a $2$-dimensional projection.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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