  Semi-supervised learning provides an effective paradigm for leveraging
unlabeled data to improve a model's performance. Among the many strategies
proposed, graph-based methods have shown excellent properties, in particular
since they allow to solve directly the transductive tasks according to Vapnik's
principle and they can be extended efficiently for inductive tasks. In this
paper, we propose a novel approach for the transductive semi-supervised
learning, using a complete bipartite edge-weighted graph. The proposed approach
uses the regularized optimal transport between empirical measures defined on
labelled and unlabelled data points in order to obtain an affinity matrix from
the optimal transport plan. This matrix is further used to propagate labels
through the vertices of the graph in an incremental process ensuring the
certainty of the predictions by incorporating a certainty score based on
Shannon's entropy. We also analyze the convergence of our approach and we
derive an efficient way to extend it for out-of-sample data. Experimental
analysis was used to compare the proposed approach with other label propagation
algorithms on 12 benchmark datasets, for which we surpass state-of-the-art
results. We release our code.
