Personalized PageRank with Node-dependent Restart

TL;DR

This paper introduces two novel generalizations of Personalized PageRank with node-dependent restart probabilities, providing new insights into their properties and relationships, including symmetry between direct and reverse measures.

Contribution

The paper proposes two new node-dependent restart schemes for Personalized PageRank and derives their elegant mathematical relationships and symmetry properties.

Findings

Both generalizations unify with the original when restart probability is constant.

Derived symmetry property links direct and reverse Personalized PageRanks.

Discussed special cases of restart probabilities and distributions.

Abstract

Personalized PageRank is an algorithm to classify the improtance of web pages on a user-dependent basis. We introduce two generalizations of Personalized PageRank with node-dependent restart. The first generalization is based on the proportion of visits to nodes before the restart, whereas the second generalization is based on the probability of visited node 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 the 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.