  The elastic-net is among the most widely used types of regularization
algorithms, commonly associated with the problem of supervised generalized
linear model estimation via penalized maximum likelihood. Its nice properties
originate from a combination of $\ell_1$ and $\ell_2$ norms, which endow this
method with the ability to select variables taking into account the
correlations between them. In the last few years, semi-supervised approaches,
that use both labeled and unlabeled data, have become an important component in
the statistical research. Despite this interest, however, few researches have
investigated semi-supervised elastic-net extensions. This paper introduces a
novel solution for semi-supervised learning of sparse features in the context
of generalized linear model estimation: the generalized semi-supervised
elastic-net (s2net), which extends the supervised elastic-net method, with a
general mathematical formulation that covers, but is not limited to, both
regression and classification problems. We develop a flexible and fast
implementation for s2net in R, and its advantages are illustrated using both
real and synthetic data sets.
