14,682 research outputs found
Google matrix analysis of directed networks
In past ten years, modern societies developed enormous communication and
social networks. Their classification and information retrieval processing
become a formidable task for the society. Due to the rapid growth of World Wide
Web, social and communication networks, new mathematical methods have been
invented to characterize the properties of these networks on a more detailed
and precise level. Various search engines are essentially using such methods.
It is highly important to develop new tools to classify and rank enormous
amount of network information in a way adapted to internal network structures
and characteristics. This review describes the Google matrix analysis of
directed complex networks demonstrating its efficiency on various examples
including World Wide Web, Wikipedia, software architecture, world trade, social
and citation networks, brain neural networks, DNA sequences and Ulam networks.
The analytical and numerical matrix methods used in this analysis originate
from the fields of Markov chains, quantum chaos and Random Matrix theory.Comment: 56 pages, 58 figures. Missed link added in network example of Fig3
Asynchronous Gossip for Averaging and Spectral Ranking
We consider two variants of the classical gossip algorithm. The first variant
is a version of asynchronous stochastic approximation. We highlight a
fundamental difficulty associated with the classical asynchronous gossip
scheme, viz., that it may not converge to a desired average, and suggest an
alternative scheme based on reinforcement learning that has guaranteed
convergence to the desired average. We then discuss a potential application to
a wireless network setting with simultaneous link activation constraints. The
second variant is a gossip algorithm for distributed computation of the
Perron-Frobenius eigenvector of a nonnegative matrix. While the first variant
draws upon a reinforcement learning algorithm for an average cost controlled
Markov decision problem, the second variant draws upon a reinforcement learning
algorithm for risk-sensitive control. We then discuss potential applications of
the second variant to ranking schemes, reputation networks, and principal
component analysis.Comment: 14 pages, 7 figures. Minor revisio
PageRank Optimization by Edge Selection
The importance of a node in a directed graph can be measured by its PageRank.
The PageRank of a node is used in a number of application contexts - including
ranking websites - and can be interpreted as the average portion of time spent
at the node by an infinite random walk. We consider the problem of maximizing
the PageRank of a node by selecting some of the edges from a set of edges that
are under our control. By applying results from Markov decision theory, we show
that an optimal solution to this problem can be found in polynomial time. Our
core solution results in a linear programming formulation, but we also provide
an alternative greedy algorithm, a variant of policy iteration, which runs in
polynomial time, as well. Finally, we show that, under the slight modification
for which we are given mutually exclusive pairs of edges, the problem of
PageRank optimization becomes NP-hard.Comment: 30 pages, 3 figure
Highlighting Entanglement of Cultures via Ranking of Multilingual Wikipedia Articles
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 and 2DRank. In particular, we focus on articles related to
persons, identify top 30 persons for each rank among different editions and
analyze distinctions of their distributions over activity fields such as
politics, art, science, religion, sport for each edition. We find that local
heroes are dominant but also global heroes exist and create an effective
network representing entanglement of cultures. The Google matrix analysis of
network of cultures shows signs of the Zipf law distribution. This approach
allows to examine diversity and shared characteristics of knowledge
organization between cultures. The developed computational, data driven
approach highlights cultural interconnections in a new perspective.Comment: Published in PLoS ONE
(http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0074554).
Supporting information is available on the same webpag
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