J. Solomon, R. Rustamov, L. Guibas, and A. Butscher, Wasserstein Propagation for Semi-Supervised Learning, Proc. International Conference on Machine Learning (ICML 2014).

Abstract:

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.

Bibtex: 

@inproceedings{srgb-wpssl-14, 
    Author = {Justin Solomon and Raif Rustamov and Guibas Leonidas and Adrian Butscher}, 
    Url = {http://jmlr.org/proceedings/papers/v32/solomon14.pdf}, 
    Title = {Wasserstein Propagation for Semi-Supervised Learning}, 
    Pages = {306--314}, 
    Year = {2014}, 
    Booktitle = {Proceedings of the 31st International Conference on Machine Learning} 
   }