Reproducing Kernel Hilbert Space, Mercer's Theorem, Eigenfunctions, Nystr\" om Method, and Use of Kernels in Machine Learning: Tutorial and Survey

B Ghojogh, A Ghodsi, F Karray, M Crowley - arXiv preprint arXiv …, 2021 - arxiv.org
This is a tutorial and survey paper on kernels, kernel methods, and related fields. We start
with reviewing the history of kernels in functional analysis and machine learning. Then …

Error analysis of generalized Nyström kernel regression

H Chen, H Xia, H Huang, W Cai - Advances in Neural …, 2016 - proceedings.neurips.cc
Abstract Nystr\"{o} m method has been used successfully to improve the computational
efficiency of kernel ridge regression (KRR). Recently, theoretical analysis of Nystr\"{o} m …

Computationally efficient Nyström approximation using fast transforms

S Si, CJ Hsieh, I Dhillon - International conference on …, 2016 - proceedings.mlr.press
Our goal is to improve the\it training and\it prediction time of Nyström method, which is a
widely-used technique for generating low-rank kernel matrix approximations. When applying …

Multi-scale Nystrom method

W Lim, R Du, B Dai, K Jung, L Song… - International …, 2018 - proceedings.mlr.press
Kernel methods are powerful tools for modeling nonlinear data. However, the amount of
computation and memory required for kernel methods becomes the bottleneck when dealing …

Data-driven information-theoretic tools under a second-order statistics perspective

F Cabrera Estanyol - 2023 - upcommons.upc.edu
(English) A great deal is known about second-order statistics. For many years, most of the
signal processing problems have been addressed under the perspective of the first and …

Geometric Interpretation of Running Nystr\"{o} m-Based Kernel Machines and Error Analysis

W Li, M Liu, D Zhang - arXiv preprint arXiv:2002.08937, 2020 - arxiv.org
Recently, Nystr\"{o} m method has proved its prominence empirically and theoretically in
speeding up the training of kernel machines while retaining satisfactory performances and …