Fast Multilevel Transduction on Graphs

The recent years have witnessed a surge of interest in graphbased 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 require the computation of matrix inverse). 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, our method has explicit physical meanings with some graph intuitions. We also analyze the relationship of our method with multigrid methods, and provide a theoretical guarantee of the performance of our method. Finally the experimental results are presented to show the effectiveness of our method.