@inbook {IOPORT.05803158, author = {Baldassarre, Luca and Rosasco, Lorenzo and Barla, Annalisa and Verri, Alessandro}, title = {Vector field learning via spectral filtering.}, year = {2010}, booktitle = {Machine learning and knowledge discovery in databases. European conference, ECML PKDD 2010, Barcelona, Spain, September 20--24, 2010. Proceedings, Part I}, isbn = {978-3-642-15879-7}, pages = {56-71}, publisher = {Berlin: Springer}, doi = {10.1007/978-3-642-15880-3_10}, abstract = {Summary: 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.}, identifier = {05803158}, }