Efficient Personalized PageRank Estimation for Many Sources and Many Targets

Personalized PageRank (PPR) is a measure of the importance of a node in a graph from the perspective of another node (we call these nodes the target and the source, respectively). PPR has been used in many applications, such as offering a Twitter user (the source) personalized recommendations of who to follow (targets deemed important by PPR). Computing PPR at scale is infeasible for networks like Twitter, so many estimation algorithms have been proposed. Here we explore two methods for estimating PPR of many source/target pairs. Our first method is based on the state-of-the-art PPR estimator for a single source/target pair. We extend this method to the cases of many sources and/or many targets by eliminating repeated computations that may occur when using existing algorithms separately for each source or each target. Our second method considers computation of a source's PPR when the PPR for a set of nodes, called the known set, are given. If the known set is chosen appropriately, we can compute the source's PPR on a smaller graph. At a high level, both approaches can be viewed as dimensionality reduction methods in which quantities used to compute PPR are shared among sources and/or targets by exploiting certain graph characteristics. Moving forward, we aim to develop a deeper understanding of how PPR vectors -- a high-dimensional set of objects -- are related. This may in turn help us understand how information is organized in modern networks.