SoSe 2014: M-TANI: Big Data Analytics
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1 SoSe 4: M-TANI: Big Dt Anltics Lecture 7 8/6/4 Sed Izberovic Dr. Nikolos Korfitis
2 Agend Recp fro the previous session Topic specific PgeRnk TrustRnk (Stnford slides) Link Sp (Stnford slides) Hpertext Induced Topic Selection (Stnford slides) Hubs nd Authorities (Stnford slides)
3 PgeRnk Principle of votes The iportnce r j of pge j is the su of the votes on its in-links The weight of ech link is r j, with n the su of outlinks fro the pge n j The rnk for pge j is defined b: d i is the out-degree of the pge i r j = r i d i i j A vote fro iportnt pge is ore worth then vote fro not-iportnt pge fro []
4 PgeRnk The flow equtions r j = i j cn be rewritten s r = M r The rnk vector r is n eigenvector of the stochstic web trix M M is colun stochstic trix The coluns su to We cn now efficientl solve for r with the Power itertion ethod r i d i fro []
5 Power Itertion Method Power Itertion Suppose there re N web pges Initilize: r = N N Iterte: r t+ = M r t Stop when r t+ r t < ε fro []
6 PgeRnk Probles: Spider Trps Power Itertion Set r j = r j = i j r i d i d i is the out-degree of the pge i = fro []
7 PgeRnk Probles: Spider Trps Power Itertion Set r j = r j = i j r i d i d i is the out-degree of the pge i = fro []
8 PgeRnk Probles: Spider Trps Power Itertion Set r j = r j = i j r i d i d i is the out-degree of the pge i = fro []
9 Spider Trps Solution Teleports With prob. β, follow link t rndo With prob. β, jup to soe rndo pge fro []
10 PgeRnk Probles: Ded Ends Power Itertion Set r j = r j = i j r i d i d i is the out-degree of the pge i = fro []
11 PgeRnk Probles: Ded Ends Power Itertion Set r j = r j = i j r i d i d i is the out-degree of the pge i = fro []
12 PgeRnk Probles: Ded Ends Power Itertion Set r j = r j = i j r i d i d i is the out-degree of the pge i = fro []
13 PgeRnk Probles: Ded Ends Power Itertion Set r j = r j = i j r i d i d i is the out-degree of the pge i = Mtrix is not colun stochstic fro []
14 Ded Ends Solution Teleports Follow rndo teleport links with probbilit. fro ded-ends fro []
15 Google Mtrix PgeRnk eqution r j = i j β r i d i + ( β) N With prob. β, follow link t rndo With prob. β, jup to soe rndo pge Google Mtrix A : All entries re N A = βm + ( β) N N N r = A r Power Itertion works fro []
16 Google Mtrix Exple β =.8 A =.8 +. A = fro []
17 Google Mtrix Exple A = Power Itertion = fro []
18 Google Mtrix Exple A = Power Itertion = fro []
19 Google Mtrix Exple A = Power Itertion = fro []
20 PgeRnk Probles Mesures generic populrit of pge Ignores topic specific uthorities Solution: Topic Specific/Sensitive PgeRnk fro []
21 Topic Specific PgeRnk Gol: Evlute Web pges not just ccording to their populrit, but b how close the re to prticulr topic, e.g. sports or histor Allows serch queries to be nswered bsed on interests of the user Exple: Serch quer = jgur fro [] nd []
22 Topic Specific PgeRnk Ide: bising the PgeRnk to fvor pges tht shre se topic Difference to the stndrd PgeRnk Stndrd PgeRnk Teleport cn go to n pge with equl probbilit Topic Specific PgeRnk Teleport cn go to topic specific set of relevnt pges (teleport set) fro []
23 Topic Specific PgeRnk Wht is the teleport set S? S contins onl pges tht re relevnt to specific topic Wht re the benefits of using the teleport set? For ech teleport set S, we get different (topic specific) rnk vector r S fro []
24 Topic Specific PgeRnk Mtrix forultion Stndrd PgeRnk A = βm + ( β) N N N Topic Specific PgeRnk A ii = βm ( β) ii + ii i S S βm ii + ii i S fro []
25 Topic Specific PgeRnk Mtrix forultion Vector e S ( β) ii i S e Si = S ii i S Topic Specific PgeRnk A = βm + e S fro [] nd []
26 Topic Specific PgeRnk Exple b d β =. 8; S = {b, d} c βm = Not stochstic e S = fro []
27 Topic Specific PgeRnk Exple b d β =. 8; S = {b, d} c A = + = stochstic! fro []
28 Topic Specific PgeRnk Exple b d β =. 8; S = {b, d} c A = + = stochstic! fro []
29 Topic Specific PgeRnk Exple b d β =. 8; S = {b, d} c Power Itertion = fro []
30 Topic Specific PgeRnk Exple b d β =. 8; S = {b, d} c Power Itertion = fro []
31 Topic Specific PgeRnk Exple b d β =. 8; S = {b, d} c Power Itertion = fro []
32 Topic Specific PgeRnk Exple b d β =. 8; S = {b, d} c Topic-Specific PgeRnk Stndrd PgeRnk fro [] nd []
33 Topic Specific PgeRnk Exple b d β =. 8; S = {b, d} c Topic-Specific PgeRnk Stndrd PgeRnk fro [] nd []
34 Topic Specific PgeRnk Who to crete the teleport set S? User cn pick the topic fro enu Clssif quer into topic Using context of the quer Histor of queries e.g. video ges followed b jgur Using user context Bookrks Browser Histor... fro []
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