Learning Vector Fields with Spectral Filtering

We present a class of regularized kernel methods for vector valued learning, which are based on filtering the spectrum of the kernel matrix. The considered methods include Tikhonov regularization as a special case, as well as interesting alternatives such as vector valued extensions of L2 boosting. While preserving the good statistical properties of Tikhonov regularization, some of the new algorithms allows for a much faster implementation since they require only matrix vector multiplications. We discuss the computational complexity of the different methods, taking into account the regularization parameter choice step. The results of our analysis are supported by numerical experiments.