A graph-based classification method is proposed for semi-supervised learning in the case of Euclidean data and for classification in the case of graph data. Our manifold learning technique is based on a convex optimization problem involving a convex quadratic regularization term and a concave quadratic loss function with a trade-off parameter carefully chosen so that the objective function remains convex. As shown empirically, the advantage of considering a concave loss function is that the learning problem becomes more robust in the presence of noisy labels. Furthermore, the loss function considered here is then more similar to a classification loss while several other methods treat graph-based classification problems as regression problems.
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