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Deeper Inside PageRank
 INTERNET MATHEMATICS
, 2004
"... This paper serves as a companion or extension to the “Inside PageRank” paper by Bianchini et al. [Bianchini et al. 03]. It is a comprehensive survey of all issues associated with PageRank, covering the basic PageRank model, available and recommended solution methods, storage issues, existence, uniq ..."
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Cited by 208 (4 self)
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This paper serves as a companion or extension to the “Inside PageRank” paper by Bianchini et al. [Bianchini et al. 03]. It is a comprehensive survey of all issues associated with PageRank, covering the basic PageRank model, available and recommended solution methods, storage issues, existence, uniqueness, and convergence properties, possible alterations to the basic model, suggested alternatives to the traditional solution methods, sensitivity and conditioning, and finally the updating problem. We introduce a few new results, provide an extensive reference list, and speculate about exciting areas of future research.
A survey on pagerank computing
 Internet Mathematics
, 2005
"... Abstract. This survey reviews the research related to PageRank computing. Components of a PageRank vector serve as authority weights for web pages independent of their textual content, solely based on the hyperlink structure of the web. PageRank is typically used as a web search ranking component. T ..."
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Cited by 106 (0 self)
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Abstract. This survey reviews the research related to PageRank computing. Components of a PageRank vector serve as authority weights for web pages independent of their textual content, solely based on the hyperlink structure of the web. PageRank is typically used as a web search ranking component. This defines the importance of the model and the data structures that underly PageRank processing. Computing even a single PageRank is a difficult computational task. Computing many PageRanks is a much more complex challenge. Recently, significant effort has been invested in building sets of personalized PageRank vectors. PageRank is also used in many diverse applications other than ranking. We are interested in the theoretical foundations of the PageRank formulation, in the acceleration of PageRank computing, in the effects of particular aspects of web graph structure on the optimal organization of computations, and in PageRank stability. We also review alternative models that lead to authority indices similar to PageRank and the role of such indices in applications other than web search. We also discuss linkbased search personalization and outline some aspects of PageRank infrastructure from associated measures of convergence to link preprocessing. 1.
Video Search Reranking through Random Walk over DocumentLevel Context Graph
, 2007
"... Multimedia search over distributed sources often result in recurrent images or videos which are manifested beyond the textual modality. To exploit such contextual patterns and keep the simplicity of the keywordbased search, we propose novel reranking methods to leverage the recurrent patterns to im ..."
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Cited by 57 (8 self)
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Multimedia search over distributed sources often result in recurrent images or videos which are manifested beyond the textual modality. To exploit such contextual patterns and keep the simplicity of the keywordbased search, we propose novel reranking methods to leverage the recurrent patterns to improve the initial text search results. The approach, context reranking, is formulated as a random walk problem along the context graph, where video stories are nodes and the edges between them are weighted by multimodal contextual similarities. The random walk is biased with the preference towards stories with higher initial text search scores â a principled way to consider both initial text search results and their implicit contextual relationships. When evaluated on TRECVID 2005 video benchmark, the proposed approach can improve retrieval on the average up to 32 % relative to the baseline text search method in terms of storylevel Mean Average Precision. In the peoplerelated queries, which usually have recurrent coverage across news sources, we can have up to 40 % relative improvement. Most of all, the proposed method does not require any additional input from users (e.g., example images), or complex search models for special queries (e.g., named person search).
Graph theory and networks in biology
 IET Systems Biology, 1:89 – 119
, 2007
"... In this paper, we present a survey of the use of graph theoretical techniques in Biology. In particular, we discuss recent work on identifying and modelling the structure of biomolecular networks, as well as the application of centrality measures to interaction networks and research on the hierarch ..."
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Cited by 43 (0 self)
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In this paper, we present a survey of the use of graph theoretical techniques in Biology. In particular, we discuss recent work on identifying and modelling the structure of biomolecular networks, as well as the application of centrality measures to interaction networks and research on the hierarchical structure of such networks and network motifs. Work on the link between structural network properties and dynamics is also described, with emphasis on synchronization and disease propagation. 1
and T.Leise, The $25,000,000,000 eigenvector. The linear algebra behind Google
 SIAM Review
"... Abstract. Google’s success derives in large part from its PageRank algorithm, which ranks the importance of web pages according to an eigenvector of a weighted link matrix. Analysis of the PageRank formula provides a wonderful applied topic for a linear algebra course. Instructors may assign this a ..."
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Cited by 38 (0 self)
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Abstract. Google’s success derives in large part from its PageRank algorithm, which ranks the importance of web pages according to an eigenvector of a weighted link matrix. Analysis of the PageRank formula provides a wonderful applied topic for a linear algebra course. Instructors may assign this article as a project to more advanced students or spend one or two lectures presenting the material with assigned homework from the exercises. This material also complements the discussion of Markov chains in matrix algebra. Maple and Mathematica files supporting this material can be found at www.rosehulman.edu/∼bryan.
An experimental investigation of graph kernels on a collaborative recommendation task
 Proceedings of the 6th International Conference on Data Mining (ICDM 2006
, 2006
"... This paper presents a survey as well as a systematic empirical comparison of seven graph kernels and two related similarity matrices (simply referred to as graph kernels), namely the exponential diffusion kernel, the Laplacian exponential diffusion kernel, the von Neumann diffusion kernel, the regul ..."
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Cited by 27 (7 self)
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This paper presents a survey as well as a systematic empirical comparison of seven graph kernels and two related similarity matrices (simply referred to as graph kernels), namely the exponential diffusion kernel, the Laplacian exponential diffusion kernel, the von Neumann diffusion kernel, the regularized Laplacian kernel, the commutetime kernel, the randomwalkwithrestart similarity matrix, and finally, three graph kernels introduced in this paper: the regularized commutetime kernel, the Markov diffusion kernel, and the crossentropy diffusion matrix. The kernelonagraph approach is simple and intuitive. It is illustrated by applying the nine graph kernels to a collaborativerecommendation task and to a semisupervised classification task, both on several databases. The graph methods compute proximity measures between nodes that help study the structure of the graph. Our comparisons suggest that the regularized commutetime and the Markov diffusion kernels perform best, closely followed by the regularized Laplacian kernel. 1
A Social Network Based Approach to Personalized Recommendation
 of Participatory Media Content,” ICWS
, 2008
"... Given the rapid growth of participatory media content such as blogs, there is a need to design personalized recommender systems to recommend only useful content to users. We believe that in addition to producing useful recommendations, certain insights from media research such as simplification and ..."
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Cited by 23 (8 self)
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Given the rapid growth of participatory media content such as blogs, there is a need to design personalized recommender systems to recommend only useful content to users. We believe that in addition to producing useful recommendations, certain insights from media research such as simplification and opinion diversity in recommendations should form the foundations of such recommender systems, so that the behavior of the systems can be understood more closely, and modified if necessary. We propose and evaluate such a system based on a Bayesian usermodel. We use the underlying social network of blog authors and readers to model the preference features for individual users. The initial results of our proposed solution are encouraging, and set the agenda for future research.
Updating the Stationary Vector of an Irreducible Markov Chain with an Eye on Google's PageRank
 In SIMAX
, 2004
"... An iterative algorithm based on aggregation/disaggregation principles is presented for updating the stationary distribution of a finite homogeneous irreducible Markov chain. The focus is on largescale problems of the kind that are characterized by Google's PageRank application, but the algori ..."
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Cited by 19 (7 self)
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An iterative algorithm based on aggregation/disaggregation principles is presented for updating the stationary distribution of a finite homogeneous irreducible Markov chain. The focus is on largescale problems of the kind that are characterized by Google's PageRank application, but the algorithm is shown to work well in general contexts. The algorithm is flexible in that it allows for changes to the transition probabilities as well as for the creation or deletion of states. In addition to establishing the rate of convergence, it is proven that the algorithm always converges independent of the starting vector. Results of numerical experimental are presented.
Updating Markov chains with an eye on Google’s PageRank
 SIAM J. Matrix Anal. Appl
"... Abstract. An iterative algorithm based on aggregation/disaggregation principles is presented for updating the stationary distribution of a finite homogeneous irreducible Markov chain. The focus is on largescale problems of the kind that are characterized by Google’s PageRank application, but the al ..."
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Cited by 18 (0 self)
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Abstract. An iterative algorithm based on aggregation/disaggregation principles is presented for updating the stationary distribution of a finite homogeneous irreducible Markov chain. The focus is on largescale problems of the kind that are characterized by Google’s PageRank application, but the algorithm is shown to work well in general contexts. The algorithm is flexible in that it allows for changes to the transition probabilities as well as for the creation or deletion of states. In addition to establishing the rate of convergence, it is proven that the algorithm is globally convergent. Results of numerical experiments are presented.
MULTILEVEL ADAPTIVE AGGREGATION FOR MARKOV CHAINS, WITH APPLICATION TO WEB RANKING
"... Abstract. A multilevel adaptive aggregation method for calculating the stationary probability vector of an irreducible stochastic matrix is described. The method is a special case of the adaptive smooth aggregation and adaptive algebraic multigrid methods for sparse linear systems, and is also close ..."
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Cited by 17 (8 self)
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Abstract. A multilevel adaptive aggregation method for calculating the stationary probability vector of an irreducible stochastic matrix is described. The method is a special case of the adaptive smooth aggregation and adaptive algebraic multigrid methods for sparse linear systems, and is also closely related to certain extensively studied iterative aggregation/disaggregation methods for Markov chains. In contrast to most existing approaches, our aggregation process does not employ any explicit advance knowledge of the topology of the Markov chain. Instead, adaptive agglomeration is proposed that is based on strength of connection in a scaled problem matrix, in which the columns of the original problem matrix at each recursive fine level are scaled with the current probability vector iterate at that level. Strength of connection is determined as in the algebraic multigrid method, and the aggregation process is fully adaptive, with optimized aggregates chosen in each step of the iteration and at all recursive levels. The multilevel method is applied to a set of stochastic matrices that provide models for web page ranking. Numerical tests serve to illustrate for which types of stochastic matrices the multilevel adaptive method may provide significant speedup compared to standard iterative methods. The tests also provide more insight into why Google’s PageRank model is a successful model for determining a ranking of web pages.