Vector Field Learning via Spectral Filtering
Abstract
In this paper we present and study a new class of regularized kernel methods for learning vector fields, which are based on filtering the spectrum of the kernel matrix. These methods include Tikhonov regularization as a special case, as well as interesting alternatives such as vector valued extensions of L2-Boosting. Our theoretical and experimental analysis shows that spectral filters that yield iterative algorithms, such as L2-Boosting, are much faster than Tikhonov regularization and attain the same prediction performances. Finite sample bounds for the different filters can be derived in a common framework and highlight different theoretical properties of the methods. The theory of vector valued reproducing kernel Hilbert space is a key tool in our study.
Cite
Text
Baldassarre et al. "Vector Field Learning via Spectral Filtering." European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, 2010. doi:10.1007/978-3-642-15880-3_10Markdown
[Baldassarre et al. "Vector Field Learning via Spectral Filtering." European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases, 2010.](https://mlanthology.org/ecmlpkdd/2010/baldassarre2010ecmlpkdd-vector/) doi:10.1007/978-3-642-15880-3_10BibTeX
@inproceedings{baldassarre2010ecmlpkdd-vector,
title = {{Vector Field Learning via Spectral Filtering}},
author = {Baldassarre, Luca and Rosasco, Lorenzo and Barla, Annalisa and Verri, Alessandro},
booktitle = {European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases},
year = {2010},
pages = {56-71},
doi = {10.1007/978-3-642-15880-3_10},
url = {https://mlanthology.org/ecmlpkdd/2010/baldassarre2010ecmlpkdd-vector/}
}