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.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v32-solomon14, title = {Wasserstein Propagation for Semi-Supervised Learning}, author = {Solomon, Justin and Rustamov, Raif and Guibas, Leonidas and Butscher, Adrian}, booktitle = {Proceedings of the 31st International Conference on Machine Learning}, pages = {306--314}, year = {2014}, editor = {Xing, Eric P. and Jebara, Tony}, volume = {32}, number = {1}, series = {Proceedings of Machine Learning Research}, address = {Bejing, China}, month = {22--24 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v32/solomon14.pdf}, url = {https://proceedings.mlr.press/v32/solomon14.html}, 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.} }
Endnote
%0 Conference Paper %T Wasserstein Propagation for Semi-Supervised Learning %A Justin Solomon %A Raif Rustamov %A Leonidas Guibas %A Adrian Butscher %B Proceedings of the 31st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2014 %E Eric P. Xing %E Tony Jebara %F pmlr-v32-solomon14 %I PMLR %P 306--314 %U https://proceedings.mlr.press/v32/solomon14.html %V 32 %N 1 %X 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.
RIS
TY - CPAPER TI - Wasserstein Propagation for Semi-Supervised Learning AU - Justin Solomon AU - Raif Rustamov AU - Leonidas Guibas AU - Adrian Butscher BT - Proceedings of the 31st International Conference on Machine Learning DA - 2014/01/27 ED - Eric P. Xing ED - Tony Jebara ID - pmlr-v32-solomon14 PB - PMLR DP - Proceedings of Machine Learning Research VL - 32 IS - 1 SP - 306 EP - 314 L1 - http://proceedings.mlr.press/v32/solomon14.pdf UR - https://proceedings.mlr.press/v32/solomon14.html AB - 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. ER -
APA
Solomon, J., Rustamov, R., Guibas, L. & Butscher, A.. (2014). Wasserstein Propagation for Semi-Supervised Learning. Proceedings of the 31st International Conference on Machine Learning, in Proceedings of Machine Learning Research 32(1):306-314 Available from https://proceedings.mlr.press/v32/solomon14.html.

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