Personalized PageRank with Node-dependent Restart

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

Semantic Modeling of Analytic-based Relationships with Direct Qualification

Successfully modeling state and analytics-based semantic relationships of documents enhances representation, importance, relevancy, provenience, and priority of the document. These attributes are the core elements that form the machine-based knowledge representation for documents. However, modeling document relationships that can change over time can be inelegant, limited, complex or overly burdensome for semantic technologies. In this paper, we present Direct Qualification (DQ), an approach for modeling any semantically referenced document, concept, or named graph with results from associated applied analytics. The proposed approach supplements the traditional subject-object relationships by providing a third leg to the relationship; the qualification of how and why the relationship exists. To illustrate, we show a prototype of an event-based system with a realistic use case for applying DQ to relevancy analytics of PageRank and Hyperlink-Induced Topic Search (HITS).Comment: Proceedings of the 2015 IEEE 9th International Conference on Semantic Computing (IEEE ICSC 2015

In-Degree and PageRank of Web pages: Why do they follow similar power laws?

The PageRank is a popularity measure designed by Google to rank Web pages. Experiments confirm that the PageRank obeys a `power law' with the same exponent as the In-Degree. This paper presents a novel mathematical model that explains this phenomenon. The relation between the PageRank and In-Degree is modelled through a stochastic equation, which is inspired by the original definition of the PageRank, and is analogous to the well-known distributional identity for the busy period in the M/G/1 queue. Further, we employ the theory of regular variation and Tauberian theorems to analytically prove that the tail behavior of the PageRank and the In-Degree differ only by a multiplicative factor, for which we derive a closed-form expression. Our analytical results are in good agreement with experimental data.Comment: 20 pages, 3 figures; typos added; reference adde

In-Degree and PageRank of web pages: why do they follow similar power laws?

PageRank is a popularity measure designed by Google to rank Web pages. Experiments confirm that PageRank values obey a power law with the same exponent as In-Degree values. This paper presents a novel mathematical model that explains this phenomenon. The relation between PageRank and In-Degree is modelled through a stochastic equation, which is inspired by the original definition of PageRank, and is analogous to the well-known distributional identity for the busy period in the $M/G/1$ queue. Further, we employ the theory of regular variation and Tauberian theorems to analytically prove that the tail distributions of PageRank and In-Degree differ only by a multiple factor, for which we derive a closed-form expression. Our analytical results are in good agreement with experimental data

Asymptotic analysis for personalized Web search

Personalized PageRank is used in Web search as an importance measure for Web documents. The goal of this paper is to characterize the tail behavior of the PageRank distribution in the Web and other complex networks characterized by power laws. To this end, we model the PageRank as a solution of a stochastic equation $R\stackrel{d}{=}\sum_{i=1}^NA_iR_i+B$, where $R_i$'s are distributed as $R$. This equation is inspired by the original definition of the PageRank. In particular, $N$ models the number of incoming links of a page, and $B$ stays for the user preference. Assuming that $N$ or $B$ are heavy-tailed, we employ the theory of regular variation to obtain the asymptotic behavior of $R$ under quite general assumptions on the involved random variables. Our theoretical predictions show a good agreement with experimental data

Entity Ranking on Graphs: Studies on Expert Finding

Todays web search engines try to offer services for finding various information in addition to simple web pages, like showing locations or answering simple fact queries. Understanding the association of named entities and documents is one of the key steps towards such semantic search tasks. This paper addresses the ranking of entities and models it in a graph-based relevance propagation framework. In particular we study the problem of expert finding as an example of an entity ranking task. Entity containment graphs are introduced that represent the relationship between text fragments on the one hand and their contained entities on the other hand. The paper shows how these graphs can be used to propagate relevance information from the pre-ranked text fragments to their entities. We use this propagation framework to model existing approaches to expert finding based on the entity's indegree and extend them by recursive relevance propagation based on a probabilistic random walk over the entity containment graphs. Experiments on the TREC expert search task compare the retrieval performance of the different graph and propagation models