  The task of classifying X-ray data is a problem of both theoretical and
clinical interest. Whilst supervised deep learning methods rely upon huge
amounts of labelled data, the critical problem of achieving a good
classification accuracy when an extremely small amount of labelled data is
available has yet to be tackled. In this work, we introduce a novel
semi-supervised framework for X-ray classification which is based on a
graph-based optimisation model. To the best of our knowledge, this is the first
method that exploits graph-based semi-supervised learning for X-ray data
classification. Furthermore, we introduce a new multi-class classification
functional with carefully selected class priors which allows for a smooth
solution that strengthens the synergy between the limited number of labels and
the huge amount of unlabelled data. We demonstrate, through a set of numerical
and visual experiments, that our method produces highly competitive results on
the ChestX-ray14 data set whilst drastically reducing the need for annotated
data.
