Wasserstein Propagation for Semi-Supervised Learning
Justin Solomon, Raif M. Rustamov, Leonidas Guibas, Adrian Butscher · 2014
Probability distributions and histograms are nat-ural representations for product ratings, traffic measurements, and other data considered in many machine learning applications. Thus, this pa-per 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 char-acterized by the moments and shapes of the his-tograms 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. 1.