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This article is cited in 7 scientific papers (total in 7 papers)
About the power law of the PageRank vector distribution. Part 2. Backley–Osthus model, power law verification for this model and setup of real search engines
A. Gasnikovab, P. Dvurechenskybc, M. Zhukovskiiad, S. Kime, S. Plaunovf, D. Smirnovf, F. Noskova a Moscow Institute of Physics and Technology, 9 Institutskiy per., Dolgoprudny, 141700, Russia
b Institute for Information Transmission Problems RAS, 19, build. 1 Bolshoy Karetny per., Moscow, 127051, Russia
c Weierstrass Institute for Applied Analysis and Stochastics, 39 Mohrenstr., Berlin, 10117, Germany
d "Yandex", 16 Lev Tolstoy str., Moscow, 119034, Russia
e National Research University Higher School of Economics, 20 Myasnitskaya str., Moscow, 101000, Russia
f State Budget Educational Institution Physics and Mathematical "School 2007", 9, build. 1 Gorchakova str., Moscow, 117042, Russia
Abstract:
In the second part of this paper, we consider the Buckley–Osthus model for the formation of a webgraph. For the networks generated according to this model, we numerically calculate the PageRank vector. We show that the components of this vector are distributed according to the power law. We also discuss the computational aspects of this model with respect to different numerical methods for the calculation of the PageRank vector, presented in the first part of the paper. Finally, we describe a general model for the web-page ranking and some approaches to solve the optimization problem arising when learning this model.
Key words:
Markov chain, ergodic theorem, multinomial distribution, measure concentration, maximum likelihood estimate, Google problem, gradient descent, automatic differentiation, power law distribution.
Received: 07.03.2017 Revised: 16.06.2017
Citation:
A. Gasnikov, P. Dvurechensky, M. Zhukovskii, S. Kim, S. Plaunov, D. Smirnov, F. Noskov, “About the power law of the PageRank vector distribution. Part 2. Backley–Osthus model, power law verification for this model and setup of real search engines”, Sib. Zh. Vychisl. Mat., 21:1 (2018), 23–45; Num. Anal. Appl., 11:1 (2018), 16–32
Linking options:
https://www.mathnet.ru/eng/sjvm666 https://www.mathnet.ru/eng/sjvm/v21/i1/p23
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Abstract page: | 435 | Full-text PDF : | 87 | References: | 51 | First page: | 11 |
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