PageRank的梯度和harnack型估计

IF 1.4 Q2 SOCIAL SCIENCES, INTERDISCIPLINARY

Network Science Pub Date : 2020-09-03 DOI:10.1017/nws.2020.34

P. Horn, Lauren M. Nelsen

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引用次数: 2

摘要

个性化PageRank由于能够捕捉网络的某些几何属性，不仅在网页排名中，而且在算法设计中也有很多用途。在本文中，我们研究了PageRank的扩散:如何改变跳跃(或传送)常数对PageRank值的影响。为此，我们证明了PageRank的梯度估计，类似于热方程正解的Li-Yau不等式(对于流形，后来的版本适用于图)。

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Gradient and Harnack-type estimates for PageRank

Abstract Personalized PageRank has found many uses in not only the ranking of webpages, but also algorithmic design, due to its ability to capture certain geometric properties of networks. In this paper, we study the diffusion of PageRank: how varying the jumping (or teleportation) constant affects PageRank values. To this end, we prove a gradient estimate for PageRank, akin to the Li–Yau inequality for positive solutions to the heat equation (for manifolds, with later versions adapted to graphs).

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来源期刊

Network Science SOCIAL SCIENCES, INTERDISCIPLINARY-

CiteScore

3.50

自引率

5.90%

发文量

期刊介绍： Network Science is an important journal for an important discipline - one using the network paradigm, focusing on actors and relational linkages, to inform research, methodology, and applications from many fields across the natural, social, engineering and informational sciences. Given growing understanding of the interconnectedness and globalization of the world, network methods are an increasingly recognized way to research aspects of modern society along with the individuals, organizations, and other actors within it. The discipline is ready for a comprehensive journal, open to papers from all relevant areas. Network Science is a defining work, shaping this discipline. The journal welcomes contributions from researchers in all areas working on network theory, methods, and data.