Sampling of surfaces and functions in high dimensional spaces

Qing Zou; Mathews Jacob

doi:10.48550/arXiv.1903.00965

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Sampling of surfaces and functions in high dimensional spaces

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Sampling of surfaces and functions in high dimensional spaces

Qing Zou and Mathews Jacob

ArXiv.org

03/03/2019

DOI: 10.48550/arXiv.1903.00965

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https://doi.org/10.48550/arXiv.1903.00965View

Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

We introduce a sampling theoretic framework for the recovery of smooth surfaces and functions living on smooth surfaces from few samples. The proposed approach can be thought of as a nonlinear generalization of union of subspace models widely used in signal processing. This scheme relies on an exponential lifting of the original data points to feature space, where the features live on union of subspaces. The low-rank property of the features are used to recover the surfaces as well as to determine the number of measurements needed to recover the surface. The low-rank property of the features also provides an efficient approach which resembles a neural network for the local representation of multidimensional functions on the surface; the significantly reduced number of parameters make the computational structure attractive for learning inference from limited labeled training data.

Details

Title: Subtitle: Sampling of surfaces and functions in high dimensional spaces
Creators: Qing Zou
Mathews Jacob
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arXiv.1903.00965
ISSN: 2331-8422
Language: English
Date posted: 03/03/2019
Academic Unit: Radiology; Electrical and Computer Engineering; Iowa Technology Institute; Iowa Neuroscience Institute; Radiation Oncology
Record Identifier: 9984071611402771

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