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Determining Factors Behind the PageRank Log-Log Plot [chapter]

Yana Volkovich, Nelly Litvak, Debora Donato
Algorithms and Models for the Web-Graph  
The difference between these two power laws is in a multiple coefficient, which depends mainly on the fraction of dangling nodes, average in-degree, the power law exponent, and damping factor.  ...  Further, we use the theory of regular variation to prove that PageRank and in-degree follow power laws with the same exponent.  ...  In Figure 4 we show the cumulative log-log plot of in-degree, and the log-log plots of the PageRank after the 1st, the 2nd, and the last power iterations for the damping factor 0.85.  ... 
doi:10.1007/978-3-540-77004-6_9 dblp:conf/waw/VolkovichLD07 fatcat:ifmera23ife5robg5tlearnzrm

Asymptotic analysis for personalized Web search

Yana Volkovich, Nelly Litvak
2010 Advances in Applied Probability  
To this end, we model the PageRank as a solution of a stochastic equation where the R i s are distributed as R. This equation is inspired by the original definition of the PageRank.  ...  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.  ...  Indeed, the plot of the PageRank with c = 0.5 is further from the in-degree log-log plot than the plot of the PageRank with c = 0.85.  ... 
doi:10.1239/aap/1275055243 fatcat:t5oafcj7kvfmrdykurjw6e3p5u

Asymptotic analysis for personalized Web search

Yana Volkovich, Nelly Litvak
2010 Advances in Applied Probability  
To this end, we model the PageRank as a solution of a stochastic equation where the R i s are distributed as R. This equation is inspired by the original definition of the PageRank.  ...  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.  ...  Indeed, the plot of the PageRank with c = 0.5 is further from the in-degree log-log plot than the plot of the PageRank with c = 0.85.  ... 
doi:10.1017/s0001867800004201 fatcat:jqfsyiof7fge3hxww5k6q6w2bq

Computing Heat Kernel Pagerank and a Local Clustering Algorithm [article]

Fan Chung, Olivia Simpson
2016 arXiv   pre-print
In this work, we present a sublinear time algorithm for approximating the heat kernel pagerank of a graph.  ...  The quantitative ranking of vertices obtained with heat kernel pagerank can be used for local clustering algorithms.  ...  The theory behind finding local cuts with heat kernel pagerank vectors was first presented in [9, 10] .  ... 
arXiv:1503.03155v3 fatcat:n7sdncolbvhjdnlzdtbc2dg2ve

Heat kernel based community detection

Kyle Kloster, David F. Gleich
2014 Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining - KDD '14  
Using this method, we propose a PageRank solution path plot to diagnose new aspects of the behavior of personalized PageRank.  ...  Personalized PageRank vectors used for many community detection and graph diffusion problems have a subtle dependence on a parameter epsilon that controls their accuracy.  ...  Acknowledgements We thank the following people for their careful reading of several early drafts: Huda Nassar, Bryan Rainey, and Varun Vasudevan.  ... 
doi:10.1145/2623330.2623706 dblp:conf/kdd/KlosterG14 fatcat:yfh5k4xgg5cyhgf56w5hkmzzv4

Big Macs and Eigenfactor scores: Don't let correlation coefficients fool you

Jevin West, Theodore Bergstrom, Carl T. Bergstrom
2010 Journal of the American Society for Information Science and Technology  
Acknowledgements We would like to thank Ben Althouse for assistance with figures 3, 5, and 6, Cosma Shalizi for helpful discussions, and Johan Bollen for numerous comments on the manuscript.  ...  In that paper, Davis aimed to determine whether measures of "popularity" such as impact factor and total citation differ substantially from measures of prestige such as the journal PageRank [4] and the  ...  Weighted PageRank and Eigenfactor are both variants of the PageRank algorithm. 2 In his paper Davis also looked at the correlation coefficient between Eigenfactor and impact factor scores.  ... 
doi:10.1002/asi.21374 fatcat:b55zk4bu45f6vldwws3jc6hi3q

Navigation by anomalous random walks on complex networks

Tongfeng Weng, Jie Zhang, Moein Khajehnejad, Michael Small, Rui Zheng, Pan Hui
2016 Scientific Reports  
Moreover, when applied to the PageRank search, we show how to inform the optimality of the PageRank search. The new 1  ...  Moreover, applying our framework to the famous PageRank search, we show how to inform the optimality of the PageRank search.  ...  This research has been supported, in part, by General Research Fund 26211515 from the Research Grants Council of Hong Kong, and Innovation and Technology Fund ITS/369/14FP from the Hong Kong Innovation  ... 
doi:10.1038/srep37547 pmid:27876855 pmcid:PMC5120342 fatcat:gclfd3khhfdkjfwpwy6jzku6qm

Local Ranking Problem on the BrowseGraph

Michele Trevisiol, Luca Maria Aiello, Paolo Boldi, Roi Blanco
2015 Proceedings of the 38th International ACM SIGIR Conference on Research and Development in Information Retrieval - SIGIR '15  
The "Local Ranking Problem" (LRP) is related to the computation of a centrality-like rank on a local graph, where the scores of the nodes could significantly differ from the ones computed on the global  ...  of applications in the state of the art.  ...  Figure 3 : 3 Growing Rings using only the nodes with highest PageRank. The plot shows the average values of the Kendall-⌧ at each step computed for all the subgraph.  ... 
doi:10.1145/2766462.2767704 dblp:conf/sigir/TrevisiolABB15 fatcat:6xzuydltdvefzfkv6dnrvxoh5y

What is the added value of negative links in online social networks?

Jérôme Kunegis, Julia Preusse, Felix Schwagereit
2013 Proceedings of the 22nd international conference on World Wide Web - WWW '13  
the positive links as a basis, with the idea that if this problem can be solved with high accuracy, then the "negative link" feature is redundant.  ...  To answer the question whether negative links have an added value for an online social network, we investigate the machine learning problem of predicting the negative links of such a network using only  ...  The research leading to these results has received funding from the European Community's Seventh Frame Programme under grant agreement n o 257859, ROBUST.  ... 
doi:10.1145/2488388.2488452 dblp:conf/www/KunegisPS13 fatcat:ucqwn2niejexhlgs6dw7s3iycu

Random-Walk Term Weighting for Improved Text Classification

Samer Hassan, Rada Mihalcea, Carmen Banea
2007 International Conference on Semantic Computing (ICSC 2007)  
This paper describes a new approach for estimating term weights in a document, and shows how the new weighting scheme can be used to improve the accuracy of a text classifier.  ...  Experiments performed on three standard classification datasets show that the new random-walk based approach outperforms the traditional term frequency approach of feature weighting.  ...  Acknowledgments This work was supported in part by a research grant from the Texas Advanced Research Program (#003594).  ... 
doi:10.1109/icsc.2007.56 dblp:conf/semco/HassanMB07 fatcat:wpyjwpp6crcyzcm6um4uboe6da

RANDOM WALK TERM WEIGHTING FOR IMPROVED TEXT CLASSIFICATION

SAMER HASSAN, RADA MIHALCEA, CARMEN BANEA
2007 International Journal of Semantic Computing (IJSC)  
This paper describes a new approach for estimating term weights in a document, and shows how the new weighting scheme can be used to improve the accuracy of a text classifier.  ...  Experiments performed on three standard classification datasets show that the new random-walk based approach outperforms the traditional term frequency approach of feature weighting.  ...  Acknowledgments This work was supported in part by a research grant from the Texas Advanced Research Program (#003594).  ... 
doi:10.1142/s1793351x07000263 fatcat:tvjdmo2kavgirn2w7kbo6yqmrq

Random-Walk Term Weighting for Improved Text Classification

Samer Hassan, Rada Mihalcea, Carmen Banea
2007 International Conference on Semantic Computing (ICSC 2007)  
This paper describes a new approach for estimating term weights in a document, and shows how the new weighting scheme can be used to improve the accuracy of a text classifier.  ...  Experiments performed on three standard classification datasets show that the new random-walk based approach outperforms the traditional term frequency approach of feature weighting.  ...  Acknowledgments This work was supported in part by a research grant from the Texas Advanced Research Program (#003594).  ... 
doi:10.1109/icosc.2007.4338355 fatcat:gpsgoww2h5bwnkckxnn4ufdkly

GraphSC: Parallel Secure Computation Made Easy

Kartik Nayak, Xiao Shaun Wang, Stratis Ioannidis, Udi Weinsberg, Nina Taft, Elaine Shi
2015 2015 IEEE Symposium on Security and Privacy  
Our secure matrix factorization implementation can process 1 million ratings in 13 hours, which is a multiple order-of-magnitude improvement over the only other existing attempt, which requires 3 hours  ...  Importantly, our secure version of graph-based algorithms incurs a small logarithmic overhead in comparison with the non-secure parallel version.  ...  Plots are in a log-log scale, showing the expected small increase to the number of processors P .  ... 
doi:10.1109/sp.2015.30 dblp:conf/sp/NayakWIWTS15 fatcat:ifmmdvlrd5c7nj5otbbckdne6m

PageRank in scale-free random graphs [article]

Ningyuan Chen, Nelly Litvak, Mariana Olvera-Cravioto
2014 arXiv   pre-print
We analyze the distribution of PageRank on a directed configuration model and show that as the size of the graph grows to infinity it can be closely approximated by the PageRank of the root node of an  ...  This tree approximation is in turn related to the solution of a linear stochastic fixed point equation that has been thoroughly studied in the recent literature.  ...  Figure 2 plots the empirical CDF of PagerRank on G(n), the empirical CDF of PageRank on G(n) after only k iterations, and the empirical CDF of the PageRank of the 1000 root nodes after the same k iterations  ... 
arXiv:1408.3610v1 fatcat:q7dvmmqqabhbrmss7sgrqt6fr4

PageRank in Scale-Free Random Graphs [chapter]

Ningyuan Chen, Nelly Litvak, Mariana Olvera-Cravioto
2014 Lecture Notes in Computer Science  
We analyze the distribution of PageRank on a directed configuration model and show that as the size of the graph grows to infinity it can be closely approximated by the PageRank of the root node of an  ...  This tree approximation is in turn related to the solution of a linear stochastic fixed point equation that has been thoroughly studied in the recent literature.  ...  Figure 2 plots the empirical CDF of PagerRank on G(n), the empirical CDF of PageRank on G(n) after only k iterations, and the empirical CDF of the PageRank of the 1000 root nodes after the same k iterations  ... 
doi:10.1007/978-3-319-13123-8_10 fatcat:mnsu6r6ixneulh7pynlazxfvky
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