Abstract : Domain adaptation from one data space (or domain) to the other is one of the most challenging tasks of modern data analytics. If the adaptation is done cor-rectly, models built on a specific data space become able to process data depicting the same semantic concepts (the classes), but observed by another observation system with its own specificities. In this paper, we propose an optimal transporta-tion model that aligns the representations in the source and target domains. We learn a transportation plan matching both PDFs and constrain labeled samples in the source domain to remain close during transport with a non convex group regularization. This way, we exploit at the same time the labeled information in the source (the same that will be used by the classifier after adaptation) and the unlabeled distributions observed in both domains. We propose an efficient majoration-minimization algorithm to solve the resultaing optimization problem and discuss its convergence. Numerical experiments of real data show the interest of the method, that outperforms state-of-the-art approaches.