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arXiv 2004.07234cs.LGstat.ML
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LOCA:LOcal Conformal Autoencoder,用于标准化数据坐标

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

摘要:

我们提出了一种基于深度学习的方法,用于从科学测量中获取标准化的数据坐标。数据观测被建模为来自底层黎曼流形的未知非线性变形的样本,该变形由几个归一化的潜变量参数化。通过利用重复测量采样策略,我们提出了一种学习$\mathbb{R}^d$中的嵌入的方法,该方法与流形的潜变量等距。这些数据坐标在变量的平滑变化下是不变的,使得同一现象的不同仪器观测之间能够匹配。我们的嵌入是使用LOcal保形自动编码器(LOCA)获得的,LOCA是一种通过使用局部z评分过程来构建嵌入以纠正变形的算法,同时保留相关的几何信息。我们在各种模型设置上展示了LOCA的等距嵌入特性,并观察到它表现出有前途的内插和外推能力。最后,我们将LOCA应用于单站点Wi-Fi定位数据,并应用于基于$2$维投影的$3$维曲面估计。

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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