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Strong Localization in Personalized PageRank Vectors [chapter]

Huda Nassar, Kyle Kloster, David F. Gleich
2015 Lecture Notes in Computer Science  
We derive an upperbound on the number of entries necessary to approximate a personalized PageRank vector in graphs with skewed degree sequences.  ...  The personalized PageRank diffusion is a fundamental tool in network analysis tasks like community detection and link prediction.  ...  Localization in Personalized PageRank The example in Sect. 2 demonstrates that there exist seeded PageRank vectors that are non-local.  ... 
doi:10.1007/978-3-319-26784-5_15 fatcat:jwus6sz2ebfhljw2jeqv6xcpfu

Higher Order Information Identifies Tie Strength [article]

Arnab Sarker, Jean-Baptiste Seby, Austin R. Benson, Ali Jadbabaie
2021 arXiv   pre-print
A key question in the analysis of sociological processes on networks is to identify pairs of individuals who have strong or weak social ties.  ...  Empirically, we find that Edge PageRank outperforms standard measures in identifying tie strength in several large-scale social networks.  ...  Figure 9 : 9 Personalized Edge PageRank Decomposition of (1, 2), a strong tie in the network.  ... 
arXiv:2108.02091v1 fatcat:6mgfucktgvgwjhedm4rywz7k6e

Local Partitioning for Directed Graphs Using PageRank

Reid Andersen, Fan Chung, Kevin Lang
2008 Internet Mathematics  
In particular, we prove that by computing a personalized PageRank vector in a directed graph, starting from a single seed vertex within a set S that has conductance at most α, and by performing a sweep  ...  In this paper, we present a generalization of a local partitioning algorithm for undirected graphs to strongly connected directed graphs.  ...  Computing personalized PageRank in the PageRank Markov chain To apply our local partitioning theorem to M β , we must compute a personalized PageRank vector in the Markov chain M β .  ... 
doi:10.1080/15427951.2008.10129297 fatcat:6i3h2hm3kbefll2fwyuaho7yxm

Approximating Personalized PageRank with Minimal Use of Web Graph Data

David Gleich, Marzia Polito
2006 Internet Mathematics  
In practice, and relative to the size of the web, only a small number of pages have a non-negligible personalized PageRank score.  ...  In this paper, we consider the problem of calculating fast and accurate approximations to the personalized PageRank score ([8, 16]) of a webpage.  ...  Acknowledgments We are grateful to Ara Nefian and Carole Dulong for the numerous discussions and inputs in the definition and development stages of this project.  ... 
doi:10.1080/15427951.2006.10129128 fatcat:upj2qb3z35cp7gqgw74ndjyxny

Distributed Calculation of PageRank Using Strongly Connected Components [chapter]

Michael Brinkmeier
2006 Lecture Notes in Computer Science  
We provide an approach to distribute the calculation of PageRank, by splitting the graph into its strongly connected components.  ...  Depending on the structure of the WWW, this approach approach may be used to calculate the ranking on several components in parallel, and allows to split the problem intio significantly small subproblems  ...  The factor 1/ (1 − d) is required, because in the iteration the personalization vector is multiplied by (1 − d) .  ... 
doi:10.1007/11749776_3 fatcat:zqfhumitpngd5os3jkh37zbabu

A flexible PageRank-based graph embedding framework closely related to spectral eigenvector embeddings [article]

Disha Shur, Yufan Huang, David F. Gleich
2022 arXiv   pre-print
We study a simple embedding technique based on a matrix of personalized PageRank vectors seeded on a random set of nodes.  ...  representation, and (3) uses a relatively small number of PageRank vectors compared to the size of the networks.  ...  When the teleportation distribution v has support size 1, the PageRank problem is also called personalized PageRank problem and the corresponding solution x is personalized PageRank vector or a seeded  ... 
arXiv:2207.11321v1 fatcat:cnctb4mppjbe3l6zxua4v27n6a

Highlighting Entanglement of Cultures via Ranking of Multilingual Wikipedia Articles

Young-Ho Eom, Dima L. Shepelyansky, Matjaz Perc
2013 PLoS ONE  
How different cultures evaluate a person? Is an important person in one culture is also important in the other culture? We address these questions via ranking of multilingual Wikipedia articles.  ...  With three ranking algorithms based on network structure of Wikipedia, we assign ranking to all articles in 9 multilingual editions of Wikipedia and investigate general ranking structure of PageRank, CheiRank  ...  We thank Pablo Aragón and Andreas Kaltenbrunner for the list of persons in EN, IT, NL which we used to obtain supporting Figs.S1,S2,S3 in File S1.  ... 
doi:10.1371/journal.pone.0074554 pmid:24098338 pmcid:PMC3789750 fatcat:rdrzboxxczgrvmmz37xkwzfawe

Community Detection Using Time-Dependent Personalized PageRank

Haim Avron, Lior Horesh
2015 International Conference on Machine Learning  
We present an efficient local algorithm for approximating a graph diffusion that generalizes both the celebrated personalized PageRank and its recent competitor/companion -the heat kernel.  ...  Our experimental results suggest that it produces rankings that are distinct and competitive with the ones produced by high quality implementations of personalized PageRank and localized heat kernel, and  ...  of personalized PageRank and localized heat kernel.  ... 
dblp:conf/icml/AvronH15 fatcat:xiym4oigx5gfdf65l63ynw6ksq

On the initial value of PageRank [article]

Krishanu Deyasi
2022 arXiv   pre-print
In addition, we have shown that localization of PageRank depends on the intrinsic, non-network contribution.  ...  PageRank is used by Google for ranking web pages to present search results for a user query.  ...  The PageRank vector is not localized in PGP network.  ... 
arXiv:1609.00004v2 fatcat:cziq3hvfvjglrnqm25acbyn624

Anti-differentiating approximation algorithms: A case study with min-cuts, spectral, and flow

David F. Gleich, Michael W. Mahoney
2014 International Conference on Machine Learning  
of the popular PageRank vector, and the highly effective "push" procedure for computing an approximation to personalized PageRank.  ...  We explore this concept with a case study of approximation algorithms for finding locally-biased partitions in data graphs, demonstrating connections between min-cut objectives, a personalized version  ...  Consider the personalized PageRank problem (I − βAD −1 )x = (1 − β)v, where v = e i is localized onto a single node. If A is a connected, undirected graph, then x a strictly positive solution vector.  ... 
dblp:conf/icml/GleichM14 fatcat:3z2hi2xopvfpnmnimdcyvuqnxi

Optimizing Personalized Retrieval System Based on Web Ranking [chapter]

Hao-ming Wang, Ye Guo, Bo-qin Feng
2006 Lecture Notes in Computer Science  
This paper drew up a personalized recommender system model combined the text categorization with the pagerank.  ...  The features were extracted in order to form the feature vector, which would be used in computing the difference between the documents or keywords with the user's interests and the given domain.  ...  It drew up a new personalization model, which combine the text categorization with pagerank computation.  ... 
doi:10.1007/11753728_63 fatcat:h2fnju5mazdhdegz26uo7z3gn4

Cluster Based Personalized Search [chapter]

Hyun Chul Lee, Allan Borodin
2009 Lecture Notes in Computer Science  
We propose some formal criteria for evaluating such personalized ranking algorithms and provide some preliminary experiments in support of our analysis.  ...  We study personalized web ranking algorithms based on the existence of document clusterings.  ...  Topic-Sensitive PageRank algorithm is not monotone and not local. In contrast we show that our PSP algorithm does enjoy the monotone and local properties. Theorem 4.  ... 
doi:10.1007/978-3-540-95995-3_14 fatcat:5amsgsrfrvd4lajtquby4ecuyi

Random Walks on Simplicial Complexes and the normalized Hodge 1-Laplacian [article]

Michael T. Schaub and Austin R. Benson and Paul Horn and Gabor Lippner and Ali Jadbabaie
2019 arXiv   pre-print
Specifically, we use our normalized Hodge Laplacian to derive spectral embeddings for examining trajectory data of ocean drifters near Madagascar and also develop a generalization of personalized PageRank  ...  The PageRank vector in (B) is localized and has small magnitude. The vector in (C) is almost localized but has large magnitude.  ...  In the following, we will thus concentrate on personalized PageRank vectors with a teleportation vector x localized on a particular edge [i, j] .  ... 
arXiv:1807.05044v5 fatcat:wxtoo3xvgrbgpdqskkishjhbfy

Multiscale Matrix Sampling and Sublinear-Time PageRank Computation

Christian Borgs, Michael Brautbar, Jennifer Chayes, Shang-Hua Teng
2014 Internet Mathematics  
Our second main technical contribution is a new local algorithm for approximating personalized PageRank, which is more robust than the earlier ones developed in [2, 11] and is highly efficient particularly  ...  A fundamental problem arising in many applications in Web science and social network analysis is the problem of identifying all nodes in a network whose PageRank exceeds a given threshold ∆.  ...  In Section 5, we address the problem of finding significant columns in a PageRank matrix by giving a robust local algorithm for approximating personalized PageRank vectors.  ... 
doi:10.1080/15427951.2013.802752 fatcat:zkecc6d2cfhvpoe4gv4xd374de

Multiple Local Community Detection

Alexandre Hollocou, Thomas Bonald, Marc Lelarge
2018 Performance Evaluation Review  
The new nodes are selected by some local clustering of the graph embedded in a vector space of low dimension.  ...  In this paper, we introduce a new algorithm for detecting multiple local communities, possibly overlapping, by expanding the initial seed set.  ...  Personalized PageRank The Personalized PageRank is certainly the most common score used for local community detection [16] . It is based on a random walk with restart.  ... 
doi:10.1145/3199524.3199537 fatcat:wxqo4hwu6vg33gswftxtcqxh5e
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