The Push Algorithm for Spectral Ranking

The push algorithm was proposed first by Jeh and Widom in the context of personalized PageRank computations (albeit the name "push algorithm" was actually used by Andersen, Chung and Lang in a subsequent paper). In this note we describe the algorithm at a level of generality that make the computation of the spectral ranking of any nonnegative matrix possible. Actually, the main contribution of this note is that the description is very simple (almost trivial), and it requires only a few elementary linear-algebra computations. Along the way, we give new precise ways of estimating the convergence of the algorithm, and describe some of the contribution of the existing literature, which again turn out to be immediate when recast in our framework.