Vector Field Learning via Spectral Filtering

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.