  In this paper, we tackle the transductive semi-supervised learning problem
that aims to obtain label predictions for the given unlabeled data points
according to Vapnik's principle. Our proposed approach is based on optimal
transport, a mathematical theory that has been successfully used to address
various machine learning problems, and is starting to attract renewed interest
in semi-supervised learning community. The proposed approach, Optimal Transport
Propagation (OTP), performs in an incremental process, label propagation
through the edges of a complete bipartite edge-weighted graph, whose affinity
matrix is constructed from the optimal transport plan between empirical
measures defined on labeled and unlabeled data. OTP ensures a high degree of
predictions certitude by controlling the propagation process using a certainty
score based on Shannon's entropy. We also provide a convergence analysis of our
algorithm. Experiments task show the superiority of the proposed approach over
the state-of-the-art. We make our code publicly available.
