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Kernel mode decomposition and the pr...

Owhadi, Houman.

Kernel mode decomposition and the programming of kernels

Record Type:	Electronic resources : Monograph/item
Title/Author:	Kernel mode decomposition and the programming of kernelsby Houman Owhadi, Clint Scovel, Gene Ryan Yoo.
Author:	Owhadi, Houman.
other author:	Scovel, Clint.
Published:	Cham :Springer International Publishing :2021.
Description:	x, 118 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Regression analysis.
Online resource:	https://doi.org/10.1007/978-3-030-82171-5
ISBN:	9783030821715$q(electronic bk.)

Kernel mode decomposition and the programming of kernels
Owhadi, Houman.

Kernel mode decomposition and the programming of kernels[electronic resource] /by Houman Owhadi, Clint Scovel, Gene Ryan Yoo. - Cham :Springer International Publishing :2021. - x, 118 p. :ill. (some col.), digital ;24 cm. - Surveys and tutorials in the applied mathematical sciences,v. 82199-4773 ;. - Surveys and tutorials in the applied mathematical sciences ;v.7..

Introduction -- Review -- The mode decomposition problem -- Kernel mode decomposition networks (KMDNets) -- Additional programming modules and squeezing -- Non-trigonometric waveform and iterated KMD -- Unknown base waveforms -- Crossing frequencies, vanishing modes, and noise -- Appendix.

This monograph demonstrates a new approach to the classical mode decomposition problem through nonlinear regression models, which achieve near-machine precision in the recovery of the modes. The presentation includes a review of generalized additive models, additive kernels/Gaussian processes, generalized Tikhonov regularization, empirical mode decomposition, and Synchrosqueezing, which are all related to and generalizable under the proposed framework. Although kernel methods have strong theoretical foundations, they require the prior selection of a good kernel. While the usual approach to this kernel selection problem is hyperparameter tuning, the objective of this monograph is to present an alternative (programming) approach to the kernel selection problem while using mode decomposition as a prototypical pattern recognition problem. In this approach, kernels are programmed for the task at hand through the programming of interpretable regression networks in the context of additive Gaussian processes. It is suitable for engineers, computer scientists, mathematicians, and students in these fields working on kernel methods, pattern recognition, and mode decomposition problems.

ISBN: 9783030821715$q(electronic bk.)

Standard No.: 10.1007/978-3-030-82171-5doiSubjects--Topical Terms:

181872
Regression analysis.

LC Class. No.: QA278.2 / .O84 2021

Dewey Class. No.: 519.536

Kernel mode decomposition and the programming of kernels
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505 0 $a Introduction -- Review -- The mode decomposition problem -- Kernel mode decomposition networks (KMDNets) -- Additional programming modules and squeezing -- Non-trigonometric waveform and iterated KMD -- Unknown base waveforms -- Crossing frequencies, vanishing modes, and noise -- Appendix.
520 $a This monograph demonstrates a new approach to the classical mode decomposition problem through nonlinear regression models, which achieve near-machine precision in the recovery of the modes. The presentation includes a review of generalized additive models, additive kernels/Gaussian processes, generalized Tikhonov regularization, empirical mode decomposition, and Synchrosqueezing, which are all related to and generalizable under the proposed framework. Although kernel methods have strong theoretical foundations, they require the prior selection of a good kernel. While the usual approach to this kernel selection problem is hyperparameter tuning, the objective of this monograph is to present an alternative (programming) approach to the kernel selection problem while using mode decomposition as a prototypical pattern recognition problem. In this approach, kernels are programmed for the task at hand through the programming of interpretable regression networks in the context of additive Gaussian processes. It is suitable for engineers, computer scientists, mathematicians, and students in these fields working on kernel methods, pattern recognition, and mode decomposition problems.
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650 2 4 $a Approximations and Expansions. $3 281039
700 1 $a Scovel, Clint. $3 910930
700 1 $a Yoo, Gene Ryan. $3 910931
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