LEADER 03543nam 22005655 450 001 9910520085603321 005 20260812170820.0 010 $a3-030-82171-4 024 7 $a10.1007/978-3-030-82171-5 035 $a(MiAaPQ)EBC6838762 035 $a(Au-PeEL)EBL6838762 035 $a(CKB)20275205600041 035 $a(OCoLC)1292360497 035 $a(PPN)259386367 035 $a(DE-He213)978-3-030-82171-5 035 $a(EXLCZ)9920275205600041 100 $a20211203d2021 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aKernel Mode Decomposition and the Programming of Kernels /$fby Houman Owhadi, Clint Scovel, Gene Ryan Yoo 205 $a1st ed. 2021. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2021. 215 $a1 online resource (125 pages) 225 1 $aSurveys and Tutorials in the Applied Mathematical Sciences,$x2199-4773 ;$v8 311 08$aPrint version: Owhadi, Houman Kernel Mode Decomposition and the Programming of Kernels Cham : Springer International Publishing AG,c2022 9783030821708 327 $aIntroduction -- 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. 330 $aThis monograph demonstrates a new approach to the classical mode decomposition problem through nonlinear regression models, which achieve near-machine precision in the recovery of the modes. The presentation includes a review of generalized additive models, additive kernels/Gaussian processes, generalized Tikhonov regularization, empirical mode decomposition, and Synchrosqueezing, which are all related to and generalizable under the proposed framework. Although kernel methods have strong theoretical foundations, they require the prior selection of a good kernel. While the usual approach to this kernel selection problem is hyperparameter tuning, the objective of this monograph is to present an alternative (programming) approach to the kernel selection problem while using mode decomposition as a prototypical pattern recognition problem. In this approach, kernels are programmed for the task at hand through the programming of interpretable regression networks in the contextof additive Gaussian processes. It is suitable for engineers, computer scientists, mathematicians, and students in these fields working on kernel methods, pattern recognition, and mode decomposition problems. 410 0$aSurveys and Tutorials in the Applied Mathematical Sciences,$x2199-4773 ;$v8 606 $aNeural networks (Computer science) 606 $aApproximation theory 606 $aMathematical Models of Cognitive Processes and Neural Networks 606 $aApproximations and Expansions 615 0$aNeural networks (Computer science) 615 0$aApproximation theory. 615 14$aMathematical Models of Cognitive Processes and Neural Networks. 615 24$aApproximations and Expansions. 676 $a518.2 700 $aOwhadi$b Houman$01074716 702 $aScovel$b Clint$f1955- 702 $aYoo$b Gene Ryan 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910520085603321 996 $aKernel mode decomposition and the programming of Kernels$92909943 997 $aUNINA