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


    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}