PDF Publication Title:
Text from PDF Page: 076
56 4 ⋅ random alpha pagerank encoding the distribution of teleportation parameters amongst multiple (per- haps infinite) surfers, then the PageRank model suggests α = E [A], where E [⋅] is the expectation operator. The flaw in PageRank is that using α = E [A] still does not yield the correct PageRank vector in light of the surfer values αi . We will justify this statement shortly; intuitively it arises because a single value of α condenses all surfers into a single über-surfer. Instead, we propose to give a small vote to the PageRank vector x(αi) corresponding to each random surfer and create a global metric that amalgamates this information. In other words, we want to examine the random surfer model with “α = A,” where A is a random variable modeling the users’ individual behaviors. Figure 4.1 gives a pictorial view of this change. If A is a random variable, then the PageRank vector x(A) is a random vector, and we can synthesize a new ranking measure from its statistics. We call this measure Random Alpha Pagerank (RAPr), it is pronounced “wrapper.” → x(E [A]) → E [x(A)] (a) The PageRank Model (b) Our random α PageRank model An earlier work, Constantine and Gleich [2007], introduced a means of handling multiple surfers in PageRank. This chapter extends those ideas by clarifying the presentation, expanding the computational algorithms, and compiling additional results. In particular, the previous paper used the poly- nomial chaos approach to investigate the behavior of multiple surfers algo- rithmically. In Constantine et al. [2009], we showed that the polynomial chaos and quadrature methods are equivalent in the case of PageRank. The presentation in this thesis eliminates the discussion of polynomial chaos be- yond this paragraph. Finally, Constantine [2009] explores the general setting of parameterized matrix equations with one or many parameters. In what follows, we explain and analyze the RAPr model. This model has strong connections with other path damping approaches to PageRank computation, which we show in sections 4.3.3 and 4.4.3. For the interested reader, we present our algorithms with actual Matlab code from our RAPr suite of codes. Figure 4.1 – Differences between PageRank and the Random Alpha PageRank model. The PageRank model assumes a single random surfer representing an expected user. Our model assumes that each surfer is unique with a different value of α, which we represent as a random variable A. If the function x(⋅) gives the PageRank vector for a deterministic or random α or A, respectively, we then compute the expected PageRank given the distribution for A. ⋯PDF Image | MODELS AND ALGORITHMS FOR PAGERANK SENSITIVITY
PDF Search Title:
MODELS AND ALGORITHMS FOR PAGERANK SENSITIVITYOriginal File Name Searched:
gleich-pagerank-thesis.pdfDIY 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)