MODELS AND ALGORITHMS FOR PAGERANK SENSITIVITY

PDF Publication Title:

MODELS AND ALGORITHMS FOR PAGERANK SENSITIVITY ( models-and-algorithms-for-pagerank-sensitivity )

Previous Page View | Next Page View | Return to Search List

Text from PDF Page: 087

For x(E [A]) = x(1/2), we find 11 T∞11 T x(E[A])= v+ [0 1/6 5/6] +∑( − )[0 0 1] n=2 2n 2n+1 (4.15) Thus, for this example, E [x(A)] =/ x(E [A]). For this case, the RAPr solution satisfies eT [ 1/6 7/36 23/36 ] = 1. This prop- erty is general and we next show that the vector E [x(A)] is always a proba- bility distribution. Corollary 11. If A ∼ Beta(a, b, [l , r]) with 0 ≤ l < r ≤ 1 and probability density function ρ, then E [xi (A)] > 0 and ∥E [x(A)]∥ = 1. Proof. First,E[xi(A)]≥0isbecause0≤A≤1andvi ≥0.Then,wehave ∥E[x(A)]∥ = eT 1 x(α)ρ(α)dα = 1 eTx(α)ρ(α)dα = 1, (4.16) 00 because eT x = 1 for each α and ∫ 1 ρ(α) dα = 1. 0 Finally, we show that for a certain class of pages, the expectation of RAPr is equal to PageRank with α = E [A]. Theorem12. LetA∼Beta(a,b,[l,r])with0≤l 0, where e is the vector ii with a 1 in the ith component. Taking the Neumann series for x(A) gives ∞ x (A)=eT ∑(Aj −Aj+1)Pjv=eT(A0 −A1)v=(1−A)v . (4.17) iiii j=0 Equality of the statistics follows from the linearity of the expectation opera- tor. While theorem 12 yields one condition when the expectation is the same for the random and deterministic models, the result may not be useful. Given many of the standard corrections for dangling nodes (including the methods used in this paper, see section 2.2.1),15 a graph with any dangling nodes will induce an effective graph where all nodes have an in-link. 2 4 = [1/6 5/24 5/8] T . 4.4 ⋅ the random alpha pagerank model 67 PageRank is defined as a probability vector, so this property does not change for RAPr. When a state i in P has no in-transitions (in-links)thenxi(α)=(1−α)vi aswell. 15Inthemostcommoncase,P=P ̄+ (1/n)edT and every node has an in-link.

PDF Image | MODELS AND ALGORITHMS FOR PAGERANK SENSITIVITY

PDF Search Title:

MODELS AND ALGORITHMS FOR PAGERANK SENSITIVITY

Original File Name Searched:

gleich-pagerank-thesis.pdf

DIY PDF Search: Google It | Yahoo | Bing

Cruise Ship Reviews | Luxury Resort | Jet | Yacht | and Travel Tech More Info

Cruising Review Topics and Articles More Info

Software based on Filemaker for the travel industry More Info

The Burgenstock Resort: Reviews on CruisingReview website... More Info

Resort Reviews: World Class resorts... More Info

The Riffelalp Resort: Reviews on CruisingReview website... More Info

CONTACT TEL: 608-238-6001 Email: greg@cruisingreview.com (Standard Web Page)