Document (#26354)

Author

Bryan, K.
Leise, T.

Title

¬The $25.000.000.000 eigenvector : the linear algebra behind Google

Source

SIAM review. 48(2006) no.3, S.569-581

Abstract

Google's success derives in large part from its PageRank algorithm, which ranks the importance of webpages 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.rose-hulman.edu/~bryan.

Content

Vgl. auch unter: http://www.rose-hulman.edu/~bryan/googleFinalVersionFixed.pdf.

Theme

Suchmaschinen

Object

Google

Similar documents (author)

1. Bryan, M.: Standards for text and hypermedia processing (1993) 2.18

   2.184183 = sum of:
     2.184183 = product of:
       4.368366 = sum of:
         4.368366 = weight(author_txt:bryan in 6615) [ClassicSimilarity], result of:
           4.368366 = score(doc=6615,freq=1.0), product of:
             0.7167882 = queryWeight, product of:
               1.0138843 = boost
               9.7509775 = idf(docFreq=6, maxDocs=44218)
               0.07250272 = queryNorm
             6.094361 = fieldWeight in 6615, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               9.7509775 = idf(docFreq=6, maxDocs=44218)
               0.625 = fieldNorm(doc=6615)
       0.5 = coord(1/2)
   

2. Bryan, M.: SGML: an author's guide to the Standard Generalized Markup Language (1988) 2.18

   2.184183 = sum of:
     2.184183 = product of:
       4.368366 = sum of:
         4.368366 = weight(author_txt:bryan in 7524) [ClassicSimilarity], result of:
           4.368366 = score(doc=7524,freq=1.0), product of:
             0.7167882 = queryWeight, product of:
               1.0138843 = boost
               9.7509775 = idf(docFreq=6, maxDocs=44218)
               0.07250272 = queryNorm
             6.094361 = fieldWeight in 7524, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               9.7509775 = idf(docFreq=6, maxDocs=44218)
               0.625 = fieldNorm(doc=7524)
       0.5 = coord(1/2)
   

3. Bryan, M.: SGML and HTML explained (1997) 2.18

   2.184183 = sum of:
     2.184183 = product of:
       4.368366 = sum of:
         4.368366 = weight(author_txt:bryan in 3350) [ClassicSimilarity], result of:
           4.368366 = score(doc=3350,freq=1.0), product of:
             0.7167882 = queryWeight, product of:
               1.0138843 = boost
               9.7509775 = idf(docFreq=6, maxDocs=44218)
               0.07250272 = queryNorm
             6.094361 = fieldWeight in 3350, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               9.7509775 = idf(docFreq=6, maxDocs=44218)
               0.625 = fieldNorm(doc=3350)
       0.5 = coord(1/2)
   

4. Blowers, H.; Bryan, R.: Weaving a library Web : a guide to developing children's websites (2004) 1.75

   1.7473463 = sum of:
     1.7473463 = product of:
       3.4946926 = sum of:
         3.4946926 = weight(author_txt:bryan in 4240) [ClassicSimilarity], result of:
           3.4946926 = score(doc=4240,freq=1.0), product of:
             0.7167882 = queryWeight, product of:
               1.0138843 = boost
               9.7509775 = idf(docFreq=6, maxDocs=44218)
               0.07250272 = queryNorm
             4.8754888 = fieldWeight in 4240, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               9.7509775 = idf(docFreq=6, maxDocs=44218)
               0.5 = fieldNorm(doc=4240)
       0.5 = coord(1/2)
   

5. Fast, K.; Leise, F.; Steckel, M.: Facets and controlled vocabularies : an annotated bibliography (2003) 1.26

   1.2574046 = sum of:
     1.2574046 = product of:
       2.5148091 = sum of:
         2.5148091 = weight(author_txt:leise in 2900) [ClassicSimilarity], result of:
           2.5148091 = score(doc=2900,freq=1.0), product of:
             0.69729096 = queryWeight, product of:
               9.617446 = idf(docFreq=7, maxDocs=44218)
               0.07250272 = queryNorm
             3.606542 = fieldWeight in 2900, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               9.617446 = idf(docFreq=7, maxDocs=44218)
               0.375 = fieldNorm(doc=2900)
       0.5 = coord(1/2)
   

Similar documents (content)

1. Turunen, E.: Mathematics behind fuzzy logic (1999) 0.13

   0.13190423 = sum of:
     0.13190423 = product of:
       0.82440144 = sum of:
         0.01273246 = weight(abstract_txt:this in 3924) [ClassicSimilarity], result of:
           0.01273246 = score(doc=3924,freq=1.0), product of:
             0.042212576 = queryWeight, product of:
               1.12144 = boost
               2.4130175 = idf(docFreq=10762, maxDocs=44218)
               0.015599308 = queryNorm
             0.3016272 = fieldWeight in 3924, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               2.4130175 = idf(docFreq=10762, maxDocs=44218)
               0.125 = fieldNorm(doc=3924)
         0.122725844 = weight(abstract_txt:exercises in 3924) [ClassicSimilarity], result of:
           0.122725844 = score(doc=3924,freq=1.0), product of:
             0.13256145 = queryWeight, product of:
               1.147369 = boost
               7.406428 = idf(docFreq=72, maxDocs=44218)
               0.015599308 = queryNorm
             0.9258035 = fieldWeight in 3924, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               7.406428 = idf(docFreq=72, maxDocs=44218)
               0.125 = fieldNorm(doc=3924)
         0.13672227 = weight(abstract_txt:material in 3924) [ClassicSimilarity], result of:
           0.13672227 = score(doc=3924,freq=1.0), product of:
             0.20545961 = queryWeight, product of:
               2.4741063 = boost
               5.3235674 = idf(docFreq=585, maxDocs=44218)
               0.015599308 = queryNorm
             0.6654459 = fieldWeight in 3924, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.3235674 = idf(docFreq=585, maxDocs=44218)
               0.125 = fieldNorm(doc=3924)
         0.5522209 = weight(abstract_txt:algebra in 3924) [ClassicSimilarity], result of:
           0.5522209 = score(doc=3924,freq=1.0), product of:
             0.5210853 = queryWeight, product of:
               3.940121 = boost
               8.478011 = idf(docFreq=24, maxDocs=44218)
               0.015599308 = queryNorm
             1.0597514 = fieldWeight in 3924, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               8.478011 = idf(docFreq=24, maxDocs=44218)
               0.125 = fieldNorm(doc=3924)
       0.16 = coord(4/25)
   

2. Computational information retrieval (2001) 0.12

   0.11903158 = sum of:
     0.11903158 = product of:
       0.7439474 = sum of:
         0.011254012 = weight(abstract_txt:this in 4167) [ClassicSimilarity], result of:
           0.011254012 = score(doc=4167,freq=2.0), product of:
             0.042212576 = queryWeight, product of:
               1.12144 = boost
               2.4130175 = idf(docFreq=10762, maxDocs=44218)
               0.015599308 = queryNorm
             0.2666033 = fieldWeight in 4167, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               2.4130175 = idf(docFreq=10762, maxDocs=44218)
               0.078125 = fieldNorm(doc=4167)
         0.15914299 = weight(abstract_txt:linear in 4167) [ClassicSimilarity], result of:
           0.15914299 = score(doc=4167,freq=2.0), product of:
             0.2156411 = queryWeight, product of:
               2.069547 = boost
               6.6796074 = idf(docFreq=150, maxDocs=44218)
               0.015599308 = queryNorm
             0.7379993 = fieldWeight in 4167, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               6.6796074 = idf(docFreq=150, maxDocs=44218)
               0.078125 = fieldNorm(doc=4167)
         0.08545141 = weight(abstract_txt:material in 4167) [ClassicSimilarity], result of:
           0.08545141 = score(doc=4167,freq=1.0), product of:
             0.20545961 = queryWeight, product of:
               2.4741063 = boost
               5.3235674 = idf(docFreq=585, maxDocs=44218)
               0.015599308 = queryNorm
             0.4159037 = fieldWeight in 4167, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               5.3235674 = idf(docFreq=585, maxDocs=44218)
               0.078125 = fieldNorm(doc=4167)
         0.48809895 = weight(abstract_txt:algebra in 4167) [ClassicSimilarity], result of:
           0.48809895 = score(doc=4167,freq=2.0), product of:
             0.5210853 = queryWeight, product of:
               3.940121 = boost
               8.478011 = idf(docFreq=24, maxDocs=44218)
               0.015599308 = queryNorm
             0.93669677 = fieldWeight in 4167, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               8.478011 = idf(docFreq=24, maxDocs=44218)
               0.078125 = fieldNorm(doc=4167)
       0.16 = coord(4/25)
   

3. Mather, L.A.: ¬A linear algebra measure of cluster quality (2000) 0.11

   0.10628278 = sum of:
     0.10628278 = product of:
       0.66426736 = sum of:
         0.009003209 = weight(abstract_txt:this in 4767) [ClassicSimilarity], result of:
           0.009003209 = score(doc=4767,freq=2.0), product of:
             0.042212576 = queryWeight, product of:
               1.12144 = boost
               2.4130175 = idf(docFreq=10762, maxDocs=44218)
               0.015599308 = queryNorm
             0.21328263 = fieldWeight in 4767, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               2.4130175 = idf(docFreq=10762, maxDocs=44218)
               0.0625 = fieldNorm(doc=4767)
         0.12731439 = weight(abstract_txt:linear in 4767) [ClassicSimilarity], result of:
           0.12731439 = score(doc=4767,freq=2.0), product of:
             0.2156411 = queryWeight, product of:
               2.069547 = boost
               6.6796074 = idf(docFreq=150, maxDocs=44218)
               0.015599308 = queryNorm
             0.59039944 = fieldWeight in 4767, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               6.6796074 = idf(docFreq=150, maxDocs=44218)
               0.0625 = fieldNorm(doc=4767)
         0.1374706 = weight(abstract_txt:matrix in 4767) [ClassicSimilarity], result of:
           0.1374706 = score(doc=4767,freq=2.0), product of:
             0.22696199 = queryWeight, product of:
               2.1231763 = boost
               6.8527 = idf(docFreq=126, maxDocs=44218)
               0.015599308 = queryNorm
             0.6056988 = fieldWeight in 4767, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               6.8527 = idf(docFreq=126, maxDocs=44218)
               0.0625 = fieldNorm(doc=4767)
         0.39047915 = weight(abstract_txt:algebra in 4767) [ClassicSimilarity], result of:
           0.39047915 = score(doc=4767,freq=2.0), product of:
             0.5210853 = queryWeight, product of:
               3.940121 = boost
               8.478011 = idf(docFreq=24, maxDocs=44218)
               0.015599308 = queryNorm
             0.7493574 = fieldWeight in 4767, product of:
               1.4142135 = tf(freq=2.0), with freq of:
                 2.0 = termFreq=2.0
               8.478011 = idf(docFreq=24, maxDocs=44218)
               0.0625 = fieldNorm(doc=4767)
       0.16 = coord(4/25)
   

4. Ding, Y.: Topic-based PageRank on author cocitation networks (2011) 0.09

   0.091466606 = sum of:
     0.091466606 = product of:
       0.5716663 = sum of:
         0.11028257 = weight(abstract_txt:weighted in 4348) [ClassicSimilarity], result of:
           0.11028257 = score(doc=4348,freq=3.0), product of:
             0.11708575 = queryWeight, product of:
               1.0783172 = boost
               6.9606886 = idf(docFreq=113, maxDocs=44218)
               0.015599308 = queryNorm
             0.9418958 = fieldWeight in 4348, product of:
               1.7320508 = tf(freq=3.0), with freq of:
                 3.0 = termFreq=3.0
               6.9606886 = idf(docFreq=113, maxDocs=44218)
               0.078125 = fieldNorm(doc=4348)
         0.007957787 = weight(abstract_txt:this in 4348) [ClassicSimilarity], result of:
           0.007957787 = score(doc=4348,freq=1.0), product of:
             0.042212576 = queryWeight, product of:
               1.12144 = boost
               2.4130175 = idf(docFreq=10762, maxDocs=44218)
               0.015599308 = queryNorm
             0.18851699 = fieldWeight in 4348, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               2.4130175 = idf(docFreq=10762, maxDocs=44218)
               0.078125 = fieldNorm(doc=4348)
         0.0824196 = weight(abstract_txt:ranks in 4348) [ClassicSimilarity], result of:
           0.0824196 = score(doc=4348,freq=1.0), product of:
             0.13906789 = queryWeight, product of:
               1.1751896 = boost
               7.5860133 = idf(docFreq=60, maxDocs=44218)
               0.015599308 = queryNorm
             0.59265727 = fieldWeight in 4348, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               7.5860133 = idf(docFreq=60, maxDocs=44218)
               0.078125 = fieldNorm(doc=4348)
         0.37100634 = weight(abstract_txt:pagerank in 4348) [ClassicSimilarity], result of:
           0.37100634 = score(doc=4348,freq=5.0), product of:
             0.27934918 = queryWeight, product of:
               2.3555005 = boost
               7.602543 = idf(docFreq=59, maxDocs=44218)
               0.015599308 = queryNorm
             1.3281096 = fieldWeight in 4348, product of:
               2.236068 = tf(freq=5.0), with freq of:
                 5.0 = termFreq=5.0
               7.602543 = idf(docFreq=59, maxDocs=44218)
               0.078125 = fieldNorm(doc=4348)
       0.16 = coord(4/25)
   

5. Ding, Y.; Yan, E.; Frazho, A.; Caverlee, J.: PageRank for ranking authors in co-citation networks (2009) 0.09

   0.08939739 = sum of:
     0.08939739 = product of:
       0.5587337 = sum of:
         0.08822606 = weight(abstract_txt:weighted in 3161) [ClassicSimilarity], result of:
           0.08822606 = score(doc=3161,freq=3.0), product of:
             0.11708575 = queryWeight, product of:
               1.0783172 = boost
               6.9606886 = idf(docFreq=113, maxDocs=44218)
               0.015599308 = queryNorm
             0.7535166 = fieldWeight in 3161, product of:
               1.7320508 = tf(freq=3.0), with freq of:
                 3.0 = termFreq=3.0
               6.9606886 = idf(docFreq=113, maxDocs=44218)
               0.0625 = fieldNorm(doc=3161)
         0.00636623 = weight(abstract_txt:this in 3161) [ClassicSimilarity], result of:
           0.00636623 = score(doc=3161,freq=1.0), product of:
             0.042212576 = queryWeight, product of:
               1.12144 = boost
               2.4130175 = idf(docFreq=10762, maxDocs=44218)
               0.015599308 = queryNorm
             0.1508136 = fieldWeight in 3161, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               2.4130175 = idf(docFreq=10762, maxDocs=44218)
               0.0625 = fieldNorm(doc=3161)
         0.06593568 = weight(abstract_txt:ranks in 3161) [ClassicSimilarity], result of:
           0.06593568 = score(doc=3161,freq=1.0), product of:
             0.13906789 = queryWeight, product of:
               1.1751896 = boost
               7.5860133 = idf(docFreq=60, maxDocs=44218)
               0.015599308 = queryNorm
             0.47412583 = fieldWeight in 3161, product of:
               1.0 = tf(freq=1.0), with freq of:
                 1.0 = termFreq=1.0
               7.5860133 = idf(docFreq=60, maxDocs=44218)
               0.0625 = fieldNorm(doc=3161)
         0.39820576 = weight(abstract_txt:pagerank in 3161) [ClassicSimilarity], result of:
           0.39820576 = score(doc=3161,freq=9.0), product of:
             0.27934918 = queryWeight, product of:
               2.3555005 = boost
               7.602543 = idf(docFreq=59, maxDocs=44218)
               0.015599308 = queryNorm
             1.4254768 = fieldWeight in 3161, product of:
               3.0 = tf(freq=9.0), with freq of:
                 9.0 = termFreq=9.0
               7.602543 = idf(docFreq=59, maxDocs=44218)
               0.0625 = fieldNorm(doc=3161)
       0.16 = coord(4/25)