A Unified View of Graph-based Semi-Supervised Learning: Label Propagation, Graph-Cuts, and Embeddings

Date of Submission: 
May 12, 2009
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Recent years have seen a growing number of graph-based semi-supervised learning methods. While the literature currently contains several of these methods, their relationships with one another and with other graph-based data analysis algorithms remain unclear. In this paper, we present a unified view of graph-based semi-supervised learning. Our framework unifies three important and seemingly unrelated approaches to semi-supervised learning, viz label propagation, graph cuts and manifold embeddings. We show that most existing label propagation methods solve a special case of a generalized label propagation (GLP) formulation which is a constrained quadratic program involving a graph Laplacian. Different methods arise simply based on the choice of the Laplacian and the nature of the constraints. Further, we show that semi-supervised graph-cut problems can also be viewed and solved as special cases of the GLP formulation. In addition, we show that semi-supervised non-linear manifold embedding methods also solve variants of the GLP problem and propose a novel family of semi-supervised algorithms based on existing embedding methods. Finally, we present comprehensive empirical performance evaluation of the existing label propagation methods as well as the new ones derived from manifold embedding. The new family of embedding based label propagation methods are found to be competitive on several datasets.