Learning random walks to rank nodes in graphs

Ranking nodes in graphs is of much recent interest. Edges, via the graph Laplacian, are used to encourage local smoothness of node scores in SVM-like formulations with generalization guarantees. In contrast, Page-rank variants are based on Markovian random walks. For directed graphs, there is no simple known correspondence between these views of scoring/ranking. Recent scalable algorithms for learning the Pagerank transition probabilities do not have generalization guarantees. In this paper we show some correspondence results between the Laplacian and the Pagerank approaches, and give new generalization guarantees for the latter. We enhance the Pagerank-learning approaches to use an additive margin. We also propose a general framework for rank-sensitive score-learning, and apply it to Laplacian smoothing. Experimental results are promising.