  As annotations of data can be scarce in large-scale practical problems,
leveraging unlabelled examples is one of the most important aspects of machine
learning. This is the aim of semi-supervised learning. To benefit from the
access to unlabelled data, it is natural to diffuse smoothly knowledge of
labelled data to unlabelled one. This induces to the use of Laplacian
regularization. Yet, current implementations of Laplacian regularization suffer
from several drawbacks, notably the well-known curse of dimensionality. In this
paper, we provide a statistical analysis to overcome those issues, and unveil a
large body of spectral filtering methods that exhibit desirable behaviors. They
are implemented through (reproducing) kernel methods, for which we provide
realistic computational guidelines in order to make our method usable with
large amounts of data.
