33 citations · 51 across the 22 of their papers we have counts for
12 papers · 1 filter
The role of parameter Jacobians in the stability of network outputs
Halyun Jeong, Palle E. T. Jorgensen, Hyun-Kyoung Kwon +2
In the framework of network dynamics, learning models, and neural tangent kernels (NTK), we show that the corresponding linearized dynamics leads naturally to a semigroup formulati…
Use of operator defect identities in multi-channel signal plus residual-analysis via iterated products and telescoping energy-residuals: Applications to kernels in machine learning
Palle E. T. Jorgensen, Myung-Sin Song, James F. Tian
We present a new operator theoretic framework for analysis of complex systems with intrinsic subdivisions into components, taking the form of "residuals" in general, and "telescopi…
Wavelet-Packet Content for Positive Operators
Myung-Sin Song, James Tian
We study positive operator decompositions associated with rooted trees of orthogonal projections. In this sense, the refinement tree induces an ``MRA in ''. To…
Infinite-Dimensional Stochastic Transforms and Reproducing Kernel Hilbert space
Palle E. T. Jorgensen, Myung-Sin Song, James Feng Tian
By way of concrete presentations, we construct two infinite-dimensional transforms at the crossroads of Gaussian fields and reproducing kernel Hilbert spaces (RKHS), thus leading t…
Positive Definite Kernels, Algorithms, Frames, and Approximations
Palle E. T. Jorgensen, Myung-Sin Song, James Tian
The main purpose of our paper is a new approach to design of algorithms of Kaczmarz type in the framework of operators in Hilbert space. Our applications include a diverse list of…
An Infinite Dimensional Analysis of Kernel Principal Components
Palle E. T. Jorgensen, Sooran Kang, Myung-Sin Song +1
We study non-linear data-dimension reduction. We are motivated by the classical linear framework of Principal Component Analysis. In nonlinear case, we introduce instead a new kern…