How about: “Eloquence” of the page “informativeness” of the page
Different Notions of importance
A set of simultaneous equations… Can we solve these?
Normalize after every multiplication
x The rate of convergence depends on the “eigen gap”
ss ma y ub l d h plete , as n m a ity te co onent next or uth entra comp. (See a e he onc first T lc eas il g the s incr W on n m teratio A i The e) slid
Suppose h 0 and a 0 are all initialized to 1 m>n
When the graph is disconnected, only 4 and 5 have non-zero authorities [. 923. 382] And only 1, 2 and 3 have non-zero hubs [. 5. 7. 5]CV When the components are bridged by adding one page (9) the authorities change only 4, 5 and 8 have non-zero authorities [. 853. 224. 47] And o 1, 2, 3, 6, 7 and 9 will have non-zero hubs [. 39. 49. 39. 21. 6]
or ect v gen nary i al e tatio p nci the s ! Pri es n iv ibutio G tr dis
Example: Suppose the Web graph is: M =
or n value f l eige Principa x is 1 tic matri s A stocha
Rank sink: A page or a group of pages is a rank sink if they can receive rank propagation from its parents but cannot propagate rank to other pages. Rank sink causes the loss of total ranks. Example:
Motivation comes also from random-surfer model
Example: Suppose the Web graph is: M =
Example (continued): Suppose c = 0. 8. All entries in Z are 0 and all entries in K are ¼. M* = 0. 8 (M+Z) + 0. 2 K = Compute rank by iterating MATLAB says: R : = M*x. R R(A)=. 338 R(B)=. 338 R(C)=. 6367 R(D)=. 6052
o Wh w sets ?
We can pick any pair of alternatives (even though I 1 was originally proposed with C 1 and I 2 with C 2)
We can use asynchronous iterations where the iteration uses some of the values updated in the current iteration
C A B Rank(A)=Rank(B)=Rank(C)= 0. 5774 C A B Rank(A)=0. 37 Rank(B)=0. 6672 Rank(C)=0. 6461 Moral: By referring to each other, a cluster of pages can artificially boost their rank (although the cluster has to be big enough to make an appreciable difference. Solution: Put a threshold on the number of intra-domain links that will count Counter: Buy two domains, and generate a cluster among those. .
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(From Ng et. al. ) The left most column Shows the original rank Calculation -the columns on the right are result of rank calculations when 30% of pages are randomly removed
Query relevance vs. query time co mputation tradeoff
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