Graph-based Semi-supervised Learning: Realizing Pointwise Smoothness Probabilistically

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Yuan Fang, Kevin Chang, Hady Lauw ;
Proceedings of the 31st International Conference on Machine Learning, PMLR 32(2):406-414, 2014.

Abstract

As the central notion in semi-supervised learning, smoothness is often realized on a graph representation of the data. In this paper, we study two complementary dimensions of smoothness: its pointwise nature and probabilistic modeling. While no existing graph-based work exploits them in conjunction, we encompass both in a novel framework of Probabilistic Graph-based Pointwise Smoothness (PGP), building upon two foundational models of data closeness and label coupling. This new form of smoothness axiomatizes a set of probability constraints, which ultimately enables class prediction. Theoretically, we provide an error and robustness analysis of PGP. Empirically, we conduct extensive experiments to show the advantages of PGP.

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