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Recently, ranking data with respect to the intrinsic geometric structure (manifold ranking) has received considerable attentions, with encouraging performance in many applications in pattern recognition, information retrieval and recommendation systems. Most of the existing manifold ranking methods focus on learning a ranking function that varies smoothly along the data manifold. However, beyond smoothness, a desirable ranking function should vary monotonically along the geodesics of the data manifold, such that the ranking order along the geodesics is preserved. In this paper, the authors aim to learn a ranking function that varies linearly and therefore monotonically along the geodesics of the data manifold.
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