Wasserstein Propagation for Semi-Supervised Learning


Justin Solomon, Raif Rustamov, Leonidas Guibas, Adrian Butscher ;
Proceedings of the 31st International Conference on Machine Learning, PMLR 32(1):306-314, 2014.


Probability distributions and histograms are natural representations for product ratings, traffic measurements, and other data considered in many machine learning applications. Thus, this paper introduces a technique for graph-based semi-supervised learning of histograms, derived from the theory of optimal transportation. Our method has several properties making it suitable for this application; in particular, its behavior can be characterized by the moments and shapes of the histograms at the labeled nodes. In addition, it can be used for histograms on non-standard domains like circles, revealing a strategy for manifold-valued semi-supervised learning. We also extend this technique to related problems such as smoothing distributions on graph nodes.

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