Ordinal ranking for google's pagerank

SIAM Journal on Matrix Analysis and Applications

Volumn 30, Issue 4, 2008, Pages 1677-1696

  Wills, Rebecca S ^a   Ipsen, Ilse C F ^b  

^a ROANOKE COLLEGE   (United States)

^b NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

Google matrix; Ordinal rank; PageRank; Power method; Ranking distance; Roundoff error; Stochastic matrix

Indexed keywords

GOOGLE MATRIX; ORDINAL RANK; PAGERANK; POWER METHOD; RANKING DISTANCE; ROUNDOFF ERROR; STOCHASTIC MATRIX;

ERROR ANALYSIS; INTERNET; NUMBER THEORY; SET THEORY; STOCHASTIC SYSTEMS;

MATRIX ALGEBRA;

EID: 70449368930     PISSN: 08954798     EISSN: 10957162     Source Type: Journal    
DOI: 10.1137/070698129     Document Type: Article

References (41)

1. http://www.google.com/technology/. Our Search: Google Technology.
2. R. Andersen, F. R. K. Chung, and K. J. Lang, Local partitioning for directed graphs using PageRank, in Algorithms and Models for the Web-Graph, Lecture Notes Comput. Sci. 4863, Springer Verlag, New York, 2007, pp. 166-178.
3. R. Baeza-Yates, P. Boldi, and C. Castillo, Generalizing PageRank: Damping functions for link-based ranking algorithms, in Proc. ACM SIGIR, Seattle, WA, August 2006, ACM Press, pp. 308-315.
4. P. Berkhin, A survey on PageRank computing, Internet Math., 2 (2005), pp. 73-120.
5. M. Bianchini, M. Gori, and F. Scarselli, Inside PageRank, ACM Trans. Internat. Tech., 5 (2005), pp. 92-128.
6. A. Borodin, G. O. Roberts, J. S. Rosenthal, and P. Tsaparas, Link analysis ranking: Algorithms, theory, and experiments, ACM Trans. Internat. Tech., 5 (2005), pp. 231-297. (Pubitemid 40449669)
7. C. Brezinski and M. Redivo-Zaglia, The PageRank vector: Properties, computation, approximation, and acceleration, SIAM J. Matrix Anal. Appl., 28 (2006), pp. 551-575.
8. S. Brin and L. Page, The anatomy of a large-scale hypertextual Web search engine, Comput. Networks ISDN Syst., 30 (1998), pp. 107-117.
9. P. Chen, H. Xie, S. Maslov, and S. Redner, Finding scientific gems with Google's PageRank algorithm, J. Infornmet., 1 (2007), pp. 8-15.
10. J. V. Davis and I. S. Dhillon, Estimating the global PageRank of Web communities, in KDD '06: Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, ACM Press, New York, 2006, pp. 116-125.
11. R. Dellavalle, L. Schilling, M. Rodriguez, H. V. de Sompel, and J. Bollen, Refining dermatology journal impact factors using PageRank, J. Am. Acad. Dermatol., 57 (2007), pp. 116-119.
12. N. Eiron, K. S. McCurley, and J. A. Tomlin, Ranking the Web frontier, in WWW '04: Proceedings of the 13th Conference on World Wide Web, ACM Press, New York, 2004, pp. 309-318.
13. L. Eldén, A note on the eigenvalues of the Google matrix, Technical report, LiTH-MAT-R- 04-101, Department of Mathematics, Linköping University, 2004.
14. A. Esuli and F. Sebastiani, PageRanking WordNet synsets: An application to opinion mining, in Proceedings of ACL 2007, Prague, CZ, 2007, pp. 25-27.
15. R. Fagin, R. Kumar, and D. Sivakumar, Comparing top k lists, SIAM J. Discrete Math., 17 (2003), pp. 425-431.
16. D. Gleich, http://www.stanford.edu/~dgleich/data/. Datasets, graphs and more.
17. D. Gleich, L. Zhukov, and P. Berkhin, Fast parallel PageRank: A linear system approach, Technical report, Yahoo! Inc., 2004.
18. G. H. Golub and C. Greif, An Arnoldi-type algorithm for computing PageRank, BIT, 46 (2006), pp. 759-771.
19. T. L. Griffiths, M. Steyvers, and A. Firl, Google and the mind: Predicting fluency with PageRank, Psychological Science, 18 (2007), pp. 1069-1076.
20. T. H. Haveliwala and S. D. Kamvar, The second eigenvalue of the Google matrix, Technical report 2003-20, Stanford University, 2003.
21. M. Haviv and L. V. D. Heyden, Perturbation bounds for the stationary probabilities of a finite Markov chain, Adv. Appl. Prob., 16 (1984), pp. 804-818.
22. N. J. Higham, Accuracy and Stability of Numerical Algorithms, 2nd ed., SIAM, Philadelphia, 2002.
23. I. C. F. Ipsen and T. M. Selee, PageRank computation, with special attention to dangling nodes, SIAM J. Matrix Anal. Appl., 29 (2007), pp. 1281-1296.
24. I. C. F. Ipsen and R. S. Wills, Mathematical properties and analysis of Google's PageRank, Bol. Soc. Esp. Mat. Apl., 34 (2006), pp. 191-196.
25. S. D. Kamvar, T. H. Haveliwala, C. D. Manning, and G. H. Golub, Exploiting the block structure of the Web for computing PageRank, Technical report 2003-17, Stanford University, 2003.
26. S. D. Kamvar, T. H. Haveliwala, C. D. Manning, and G. H. Golub, Extrapolation methods for accelerating PageRank computations, in The Twelfth International World Wide Web Conference, ACM Press, New York, 2003, pp. 261-270.
27. S. M. G. Kendall, Rank Correlation Methods, Charles Griffin & Company Limited, 1975.
28. A. Khalil and Y. Liu, Experiments with PageRank computation, Technical report 603, Computer Science Department at Indiana University, 2004.
29. S. J. Kirkland, Conditioning of the entries in the stationary vector of a Google-type matrix, Linear Algebra Appl., 418 (2006), pp. 665-681.
30. S. M. Kirsch, M. Gnasa, and A. B. Cremers, Beyond the Web: Retrieval in social information spaces, in ECIR, 2006, pp. 84-95.
31. A. N. Langville and C. D. Meyer, A survey of eigenvector methods for Web information retrieval, SIAM Rev., 47 (2005), pp. 135-161.
32. A. N. Langville and C. D. Meyer, Google's PageRank and Beyond: The Science of Search Engine Rankings, Princeton University Press, Princeton, NJ, 2006.
33. R. Mihalcea, P. Tarau, and E. Figa, PageRank on semantic networks, with application to word sense disambiguation, in COLING '04: Proceedings of the 20th International Conference on Computational Linguistics, Morristown, NJ, 2004, Association for Computational Linguistics.
34. J. L. Morrison, R. Breitling, D. J. Higham, and D. R. Gilbert, GeneRank: Using search engine technology for the analysis of microarray experiments, BMC Bioinformatics, 6 (2005), p. 233.
35. T. Ogita, S. M. Rump, and S. Oishi, Accurate sum and dot product, SIAM J. Sci. Comput., 26 (2005), pp. 1955-1988.
36. L. Page, S. Brin, R. Motwani, and T. Winograd, The PageRank citation ranking: Bringing order to the Web, Technical report, Stanford University, 1998.
37. S. P. Ponzetto and M. Strube, Deriving a large scale taxonomy from Wikipedia, in AAAI '07, 2007, pp. 1440-1445.
38. F. Qiu and J. Cho, Automatic identification of user interest for personalized search, in WWW '06: Proc. 15th International Conference onWorldWideWeb, ACM Press, New York, 2006, pp. 727-736.
39. T. Sarlós, A. A. Benczúr, K. Csalogány, D. Fogaras, and B. Rácz, To randomize or not to randomize: Space optimal summaries for hyperlink analysis, in WWW '06: Proc. 15th International Conference on World Wide Web, ACM Press, New York, 2006, pp. 297-306.
40. S. Serra-Capizzano, Jordan canonical form of the Google matrix: A potential contribution to the PageRank computation, SIAM J. Matrix Anal. Appl., 27 (2005), pp. 305-312.
41. T. Simonite, Google tool could search out hospital superbugs, 30 January 2008.