Tracking the random surfer: empirically measured teleportation parameters in PageRank
Proceedings of the 19th international conference on World wide web
Sensitivity and Stability of Ranking Vectors
SIAM Journal on Scientific Computing
Visualizing human genes on manifolds embedded in three-dimensional space
ACIIDS'12 Proceedings of the 4th Asian conference on Intelligent Information and Database Systems - Volume Part II
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ICSI'12 Proceedings of the Third international conference on Advances in Swarm Intelligence - Volume Part II
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The PageRank model helps evaluate the relative importance of nodes in a large graph, such as the graph of links on the world wide web. An important piece of the PageRank model is the teleportation parameter α. We explore the interaction between α and PageRank through the lens of sensitivity analysis. Writing the PageRank vector as a function of α allows us to take a derivative, which is a simple sensitivity measure. As an alternative approach, we apply techniques from the field of uncertainty quantification. Regarding a as a random variable produces a new PageRank model in which each PageRank value is a random variable. We explore the standard deviation of these variables to get another measure of PageRank sensitivity. One interpretation of this new model shows that it corrects a small oversight in the original PageRank formulation. Both of the above techniques require solving multiple PageRank problems, and thus a robust PageRank solver is needed. We discuss an inner-outer iteration for this purpose. The method is low-memory, simple to implement, and has excellent performance for a range of teleportation parameters. We show empirical results with these techniques on graphs with over 2 billion edges.