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:
Fitting MATLAB's peaks() function with a gaussian Kernel Model.
The model is f-greedy, i.e. it iteratively chooses the points where the difference to the reference function is highest and adds a new gaussian function there.
All those Gauss functions have the same width.
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.