Python implementation of the Vectorial Kernel Orthogonal Greedy Algorithm.
pip install git+https://github.com/GabrieleSantin/VKOGA.git
The algorithm is implemented as a scikit-learn Estimator, and it can be used via the fit and predict methods.
The best way to start using the algorithm is having a look at the demo notebook, which can also be executed online on Binder:
If you use this code in your work, please cite the paper
G. Santin, B. Haasdonk, Kernel methods for surrogate modeling, In: P. Benner, S. Grivet- Talocia, A. Quarteroni, G. Rozza, W. Schilders, and L. M. Silveira, editors, Model Order Reduc- tion, volume 2. De Gruyter, 2021.
@InCollection{Santin2021,
author = {Santin, Gabriele and Haasdonk, Bernard},
title = {Kernel Methods for Surrogate Modeling},
booktitle = {Model Order Reduction},
year = {2021},
editor = {Benner, Peter and Grivet-Talocia, Stefano and Quarteroni, Alfio and Rozza, Gianluigi and Schilders, Wil and Silveira, Luís Miguel},
booksubtitle = {System- and Data-Driven Methods and Algorithms},
volume = {2},
publisher = {De Gruyter},
}
For further details on the algorithm and its implementation, please refer to the following papers:
M. Pazouki and R. Schaback, Bases for kernel-based spaces, J. Comput. Appl. Math., 236, 575-588 (2011).
D. Wirtz and B. Haasdonk, A Vectorial Kernel Orthogonal Greedy Algorithm, Dolomites Res. Notes Approx., 6, 83-100 (2013).
G. Santin, D. Wittwar, B. Haasdonk, Greedy regularized kernel interpolation, ArXiv preprint 1807.09575 (2018).
T. Wenzel, G. Santin, B. Haasdonk, A novel class of stabilized greedy kernel approximation algorithms: Convergence, stability & uniform point distribution, Journal of Approximation Theory, 262:105508, (2021).
T. Wenzel, G. Santin, B. Haasdonk, Analysis of Target Data-Dependent Greedy Kernel Algorithms: Convergence Rates for f -, f · P - and f /P -Greedy., Constructive Approximation, (2022).
The original Matlab version of this software is maintained here.