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Spectral Ranking
, 2009
"... This note tries to attempt a sketch of the history of spectral ranking—a general umbrella name for techniques that apply the theory of linear maps (in particular, eigenvalues and eigenvectors) to matrices that do not represent geometric transformations, but rather some kind of relationship between e ..."
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Cited by 13 (2 self)
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This note tries to attempt a sketch of the history of spectral ranking—a general umbrella name for techniques that apply the theory of linear maps (in particular, eigenvalues and eigenvectors) to matrices that do not represent geometric transformations, but rather some kind of relationship between entities. Albeit recently made famous by the ample press coverage of Google’s PageRank algorithm, spectral ranking was devised more than fifty years ago, almost exactly in the same terms, and has been studied in psychology and social sciences. I will try to describe it in precise and modern mathematical terms, highlighting along the way the contributions given by previous scholars. Disclaimer This is is a work in progress with no claim of completeness. I have tried to collect evidence of spectral techniques in ranking from a number of sources, providing a unified mathematical framework that should make it possible to understand in a precise way the relationship between contributions. Reports of inaccuracies and missing references are more than welcome. 1
PageRank Problem, Survey And Future Research Directions
"... In this survey, we provide the most important computational methods to find the PageRank. This is a new comprehensive review of all major issues which are associated with PageRank problem, covering the basic topics, the iterative methods, lumping of nodes, the modification of lumping the nodes, ran ..."
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Cited by 5 (0 self)
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In this survey, we provide the most important computational methods to find the PageRank. This is a new comprehensive review of all major issues which are associated with PageRank problem, covering the basic topics, the iterative methods, lumping of nodes, the modification of lumping the nodes, rankone perturbation, rankr perturbation, advanced numerical linear algebra methods, conditioning, a new method by power series, and outlines for future studies.
PageRank as a Weak Tournament Solution
, 2007
"... We observe that ranking systems—a theoretical framework for web page ranking and collaborative filtering introduced by Altman and Tennenholtz—and tournament solutions—a wellstudied area of social choice theory—are strongly related. This relationship permits a mutual transfer of axioms and solutio ..."
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Cited by 4 (0 self)
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We observe that ranking systems—a theoretical framework for web page ranking and collaborative filtering introduced by Altman and Tennenholtz—and tournament solutions—a wellstudied area of social choice theory—are strongly related. This relationship permits a mutual transfer of axioms and solution concepts. As a first step, we formally analyze a tournament solution that is based on Google’s PageRank algorithm and study its interrelationships with common tournament solutions. It turns out that the PageRank set is always contained in both the Schwartz set and the uncovered set, but may be disjoint from most other tournament solutions. While PageRank does not satisfy various standard properties from the tournament literature, it can be much more discriminatory than established tournament solutions.
A ranking method based on handicaps
, 2013
"... Ranking methods are fundamental tools in many areas. Popular methods aggregate the statements of ‘experts’ in different ways. As such, there are various reasonable ranking methods, each one of them more or less adapted to the environment under consideration. This paper introduces a new method, calle ..."
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Ranking methods are fundamental tools in many areas. Popular methods aggregate the statements of ‘experts’ in different ways. As such, there are various reasonable ranking methods, each one of them more or less adapted to the environment under consideration. This paper introduces a new method, called the handicapbased method, and characterizes it through appealing properties. This method assigns not only scores to the items but also weights to the experts. Scores and weights form an equilibrium for a relationship based on the notion of handicaps. The method is, in a sense made precise in the paper, the counterpart to the counting method in environments that require intensityinvariance. Intensityinvariance is a desirable property when the intensity of the experts ’ statements has to be controlled. Otherwise, both the counting and handicapbased methods satisfy a property called homogeneity, which is a desirable property when cardinal statements matter, as is the case in many applications.
Approved by: Advisor Date
, 2014
"... Dedicated to my wife Fahima Amin Bhuyan and my son Faaris Shadmehr Amin ii ACKNOWLEDGMENTS I would first like to thank the Almighty for giving me this opportunity to pursue my PhD. I also would like to express my deep and sincere gratitude to my advisor, Dr. Hasan Jamil, for his constant encourageme ..."
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Dedicated to my wife Fahima Amin Bhuyan and my son Faaris Shadmehr Amin ii ACKNOWLEDGMENTS I would first like to thank the Almighty for giving me this opportunity to pursue my PhD. I also would like to express my deep and sincere gratitude to my advisor, Dr. Hasan Jamil, for his constant encouragement, support, and guidance in every time of need throughout my Ph.D. program. It was his faith in me, that kept me going through challenging times. In addition, I am grateful to my dissertation committee members: Dr. Russ Finley Jr. for instilling in me the value of excellence in research and for numerous brainsstorming sessions, Dr. Chandan Reddy for introducing me to the exciting world of data mining and Dr. Zaki Malik for his support and invaluable comments. I would like to express my gratitude to Anupam Bhattacharjee, who we have lost at a young age, for being an inspiration to us and epitomizing dedication in research. I also would like to thank my academic colleagues Dr. Emdad Hossain, Dr. Shazzad Hossain, Munirul Islam, Aminul Islam, Kazi Zakia Sultana, Saikat Dey and Shahriyar Hossain for their academic cooperation and
unknown title
, 2010
"... Keyphrases describe a document in a coherent and simple way, giving the prospective reader a way to quickly determine whether the document satisfies their information needs. The pervasion of huge amount of information on Web, with only a small amount of documents have keyphrases extracted, there is ..."
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Keyphrases describe a document in a coherent and simple way, giving the prospective reader a way to quickly determine whether the document satisfies their information needs. The pervasion of huge amount of information on Web, with only a small amount of documents have keyphrases extracted, there is a definite need to discover automatic keyphrase extraction systems. Typically, a document written by human develops around one or more general concepts or subconcepts. These concepts or subconcepts should be structured and semantically related with each other, so that they can form the meaningful representation of a document. Considering the fact, the phrases or concepts in a document are related to each other, a new approach for keyphrase extraction is introduced that exploits the semantic relations in the document. For measuring the semantic relations between concepts or subconcepts in the document, I present a comprehensive study aimed at using collaboratively constructed semantic resources like Wikipedia and its link structure. In particular, I introduce a graphbased keyphrase extraction system that exploits the semantic relations in the document and features such as term frequency. I evaluated the proposed system using novel measures and the results obtained compare favorably with previously published results on established benchmarks. ii