Kernel Mode Decomposition and the Programming of Kernels

Houman / Scovel Owhadi - Collection Yellow Sale 2023

118 pages, parution le 03/12/2021

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Résumé

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.

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.

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.