Personalized PageRank with node-dependent restart

Personalized PageRank is an algorithm to classify the importance of web pages on a user-dependent basis. We introduce two generalizations of Personalized PageRank with node-dependent restart. The first generalization, Occupation-Time Personalized PageRank, is based on the proportion of visits to nodes before the restart, whereas the second generalization, Location-of-Restart Personalized PageRank, is based on the proportion of time a node is visited just before the restart. In the original case of constant restart probability, the two measures coincide. We discuss interesting particular cases of restart probabilities and restart distributions. We show that both generalizations of Personalized PageRank have an elegant expression connecting the so-called direct and reverse Personalized PageRanks that yield a symmetry property of these Personalized PageRanks. Keywords: Personalized PageRank; Markov Processes with Restart; Renewal-reward Theorem