A multilevel approach for learning from labeled and unlabeled data on graphs

The recent years have witnessed a surge of interest in graph-based semi-supervised learning methods. The common denominator of these methods is that the data are represented by the nodes of a graph, the edges of which encode the pairwise similarities of the data. Despite the theoretical and empirical success, these methods have one major bottleneck which is the high computational complexity (since they usually need to solve a large-scale linear system of equations). In this paper, we propose a multilevel scheme for speeding up the traditional graph based semi-supervised learning methods. Unlike other accelerating approaches based on pure mathematical derivations (like conjugate gradient descent and Lanczos iteration) or intuitions, our method (1) has explicit physical meanings with some graph intuitions; (2) has guaranteed performance since it is closely related to the algebraic multigrid methods. Finally experimental results are presented to show the effectiveness of our method.