Lecture14

Lecture14 - Approximate Page Rank 1 Approximate Page Rank...

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Unformatted text preview: Approximate Page Rank 1 Approximate Page Rank Let pr α,s = pr ( α,s ) denote the page rank of a graph. Then pr α,s is a fixed point for the equation p = αs + (1- α ) pZ . We can compute pr α,s approximately using the recurrence relation p t +1 = αs + (1- α ) p t Z . Recall that we can rewrite our page rank equation as p = sαI I- (1- α ) Z = sα ∞ X k =0 (1- α ) k Z k While s is defined to be a probability distribution, i.e || s || 1 = 1 , we shall relax that constraint to s ( v ) ≥ for all v ∈ V ( G ) , when we are computing approximate page rank. Fact 1. pr α,s ( S ) + pr α,s ( S ) = pr α,s + s ( S ) for any S ⊆ V ( G ) Fact 2. pr ( α,s ) Z = pr ( α,sZ ) Fact 3. pr ( α,s ) = αs + (1- α ) pr ( α,sZ ) Definition 1. p’ is an-approximate of pr α,s if p = pr α,s- r for a residue function r : V → R + ∪ { } such that r ( v ) ≤ · d v for all v ∈ V Definition 2. The support of vector p is the number of non-zero values in p , denoted supp ( p ) ....
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This note was uploaded on 09/30/2011 for the course MATH 262 taught by Professor Aterras during the Fall '08 term at UCSD.

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Lecture14 - Approximate Page Rank 1 Approximate Page Rank...

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