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PageRank, a Look at Small Changes in a Line of Nodes and the Complete Graph
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. (MAM)ORCID-id: 0000-0002-1624-5147
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. (MAM)ORCID-id: 0000-0003-4554-6528
2016 (engelsk)Inngår i: Engineering Mathematics II: Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization / [ed] Sergei Silvestrov; Milica Rancic, Springer, 2016, s. 223-247Kapittel i bok, del av antologi (Fagfellevurdert)
Abstract [en]

In this article we will look at the PageRank algorithm used as part of the ranking process of different Internet pages in search engines by for example Google. This article has its main focus in the understanding of the behavior of PageRank as the system dynamically changes either by contracting or expanding such as when adding or subtracting nodes or links or groups of nodes or links. In particular we will take a look at link structures consisting of a line of nodes or a complete graph where every node links to all others. We will look at PageRank as the solution of a linear system of equations and do our examination in both the ordinary normalized version of PageRank as well as the non-normalized version found by solving corresponding linear system. We will show that using two different methods we can find explicit formulas for the PageRank of some simple link structures.

sted, utgiver, år, opplag, sider
Springer, 2016. s. 223-247
Serie
Springer Proceedings in Mathematics and Statistics, ISSN 2194-1009 ; 179
Emneord [en]
PageRank algorithm, graphs, linear system
HSV kategori
Forskningsprogram
matematik/tillämpad matematik
Identifikatorer
URN: urn:nbn:se:mdh:diva-16355Scopus ID: 2-s2.0-85012887513ISBN: 978-3-319-42104-9 (tryckt)ISBN: 978-3-319-42105-6 (tryckt)OAI: oai:DiVA.org:mdh-16355DiVA, id: diva2:1034022
Tilgjengelig fra: 2016-10-11 Laget: 2012-12-02 Sist oppdatert: 2019-01-15bibliografisk kontrollert
Inngår i avhandling
1. PageRank in Evolving Networks and Applications of Graphs in Natural Language Processing and Biology
Åpne denne publikasjonen i ny fane eller vindu >>PageRank in Evolving Networks and Applications of Graphs in Natural Language Processing and Biology
2016 (engelsk)Doktoravhandling, med artikler (Annet vitenskapelig)
Abstract [en]

This thesis is dedicated to the use of graph based methods applied to ranking problems on the Web-graph and applications in natural language processing and biology.

Chapter 2-4 of this thesis is about PageRank and its use in the ranking of home pages on the Internet for use in search engines. PageRank is based on the assumption that a web page should be high ranked if it is linked to by many other pages and/or by other important pages. This is modelled as the stationary distribution of a random walk on the Web-graph.

Due to the large size and quick growth of the Internet it is important to be able to calculate this ranking very efficiently. One of the main topics of this thesis is how this can be made more efficiently, mainly by considering specific types of subgraphs and how PageRank can be calculated or updated for those type of graph structures. In particular we will consider the graph partitioned into strongly connected components and how this partitioning can be utilized.

Chapter 5-7 is dedicated to graph based methods and their application to problems in Natural language processing. Specifically given a collection of texts (corpus) we will compare different clustering methods applied to Pharmacovigilance terms (5), graph based models for the identification of semantic relations between biomedical words (6) and modifications of CValue for the annotation of terms in a corpus.

In Chapter 8-9 we look at biological networks and the application of graph centrality measures for the identification of cancer genes. Specifically in (8) we give a review over different centrality measures and their application to finding cancer genes in biological networks and in (9) we look at how well the centrality of vertices in the true network is preserved in networks generated from experimental data.

sted, utgiver, år, opplag, sider
Västerås: Mälardalen University, 2016
Serie
Mälardalen University Press Dissertations, ISSN 1651-4238 ; 217
HSV kategori
Forskningsprogram
matematik/tillämpad matematik
Identifikatorer
urn:nbn:se:mdh:diva-33459 (URN)978-91-7485-298-1 (ISBN)
Disputas
2016-12-08, Kappa, Mälardalens högskola, Västerås, 13:15 (engelsk)
Opponent
Veileder
Tilgjengelig fra: 2016-10-24 Laget: 2016-10-24 Sist oppdatert: 2016-11-23bibliografisk kontrollert

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