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＜電子ブック＞
Kernel Mode Decomposition and the Programming of Kernels / by Houman Owhadi, Clint Scovel, Gene Ryan Yoo
(Surveys and Tutorials in the Applied Mathematical Sciences. ISSN:21994773 ; 8)

版	1st ed. 2021.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2021
本文言語	英語
大きさ	X, 118 p. 41 illus., 31 illus. in color : online resource
著者標目	*Owhadi, Houman author Scovel, Clint author Yoo, Gene Ryan author SpringerLink (Online service)
件　名	LCSH:Neural networks (Computer science)  LCSH:Approximation theory FREE:Mathematical Models of Cognitive Processes and Neural Networks FREE:Approximations and Expansions
一般注記	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 contextof 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 HTTP:URL=https://doi.org/10.1007/978-3-030-82171-5

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