  Semi-supervised classification is a great focus of interest, as in real-world
scenarios obtaining labels is expensive, time-consuming and might require
expert knowledge. This has motivated the fast development of semi-supervised
techniques, whose performance is on a par with or better than supervised
approaches. A current major challenge for semi-supervised techniques is how to
better handle the network calibration and confirmation bias problems for
improving performance. In this work, we argue that energy models are an
effective alternative to such problems. With this motivation in mind, we
propose a hybrid framework for semi-supervised classification called CREPE
model (1-Lapla$\mathbf{C}$ian g$\mathbf{R}$aph $\mathbf{E}$nergy for
$\mathbf{P}$seudo-lab$\mathbf{E}$ls). Firstly, we introduce a new energy model
based on the non-smooth $\ell_1$ norm of the normalised graph 1-Laplacian. Our
functional enforces a sufficiently smooth solution and strengthens the
intrinsic relation between the labelled and unlabelled data. Secondly, we
provide a theoretical analysis for our proposed scheme and show that the
solution trajectory does converge to a non-constant steady point. Thirdly, we
derive the connection of our energy model for pseudo-labelling. We show that
our energy model produces more meaningful pseudo-labels than the ones generated
directly by a deep network. We extensively evaluate our framework, through
numerical and visual experiments, using six benchmarking datasets for natural
and medical images. We demonstrate that our technique reports state-of-the-art
results for semi-supervised classification.
