Generalized Optimization Framework for Graph-based Semi-supervised Learning

TL;DR

This paper introduces a unified optimization framework for graph-based semi-supervised learning, encompassing existing methods and providing new probabilistic insights and practical robustness analysis.

Contribution

It presents a generalized framework that unifies various graph-based semi-supervised learning methods and offers new probabilistic interpretations and robustness insights.

Findings

PageRank method shows robustness to regularization and label choices

Framework unifies Laplacian, Normalized Laplacian, and PageRank methods

Effective classification on Wikipedia hyper-link graph with high precision and recall

Abstract

We develop a generalized optimization framework for graph-based semi-supervised learning. The framework gives as particular cases the Standard Laplacian, Normalized Laplacian and PageRank based methods. We have also provided new probabilistic interpretation based on random walks and characterized the limiting behaviour of the methods. The random walk based interpretation allows us to explain di erences between the performances of methods with di erent smoothing kernels. It appears that the PageRank based method is robust with respect to the choice of the regularization parameter and the labelled data. We illustrate our theoretical results with two realistic datasets, characterizing di erent challenges: Les Miserables characters social network and Wikipedia hyper-link graph. The graph-based semi-supervised learning classi- es the Wikipedia articles with very good precision and perfect recall employing only the information about the hyper-text links.