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In the context of web search, a recent study identified two types of surfers: navigators and explorers [White and Drucker, 2007]. Navigators proceed roughly linearly whereas explorers frequently branch their browsing patterns and revisit previous pages before going to new links. The first behavior cor- responds to a larger value of α than the latter. This paper also contains an extensive review of relevant literature. None of these studies directly measures α or the distribution A. A recent patent from Yahoo! [Berkhin et al., 2008] describes a modification of the PageRank equations to build a “user-sensitive PageRank” system by incorporating observed page transitions and user segment modeling.10 The key idea in the patent is to modify the Markov chain transition probabilities to give higher weight to transitions observed and change the teleportation vector in light of the start points of observed transitions. These weights depend on a user segment. They also recognize the inaccuracy of a single teleportation coefficient, but model separate teleportation coefficients to and from each page on the web. Our approach differs by modeling a random Markov chain and its associated random stationary distribution. The ideas in the patent often require smoothed estimates of probabilities from observed data. Using extensions of our ideas, we could replace some of these quantities with stochastic parameters and then apply our algorithms to generate truly random instances of these user-modified Markov chains. 4.3.3 Path damping While working on the mathematics of RAPr, we discovered a strong re- lationship with path damping interpretations of the PageRank vector. Path damping models weight each path of length l in the graph with a set of coefficients that sum to 1. Mathematically, they compute a ranking vector ∞ r = ∑ ω(l)Pl v, (4.6) l=0 ∞ where ∑l=0 ω(l) = 1 [Boldi, 2005; Baeza-Yates et al., 2006]. As we show in section 4.4.3, the value E [x(A)] corresponds to a particular choice of ω(l). 4.3.4 Personalized PageRank A personalized PageRank vector is a PageRank vector targeted at a single person, or group of people [Page et al., 1999; Haveliwala, 2002; Jeh and Widom, 2003]. Consequently, the choice of α and v are more obvious in this case. Given these personalized PageRank vectors, a natural extension of our idea is to aggregate personalized PageRank vectors. One interpretation of RAPr is that it computes an aggregate personalized PageRank vector for all surfers. RAPr, however, currently constrains each personalized PageRank vector to use the same teleportation vector, v. 10 A user segment is a group of users related by a common factor. Age, sex, and interests are all possibilities. 4.3 ⋅ related work 61PDF Image | MODELS AND ALGORITHMS FOR PAGERANK SENSITIVITY
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