VKOGA

Python implementation of the Vectorial Kernel Orthogonal Greedy Algorithm.

Usage:

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:

How to cite:

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, ArXiv preprint 1911.04352 (2019).

Other implementations:

The original Matlab version of this software is maintained here.