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68 4 ⋅ random alpha pagerank the standard deviation vector could be an important input to a machine learning framework for web search or web page categorization. The correlation structure between the random ranks indicates that some of the pages form natural groups. One may explore connections between negatively correlated ranks to glean information from the underlying graph. We do not pursue this idea further, though it may aid in applications such as spam detection.5 Another application for these techniques is local site analysis. On a website such as Wikipedia, the entire graph structure is available. Further, site usage logs contain the information necessary to generate the vector v based on incoming searches. These same logs also contain the information necessary to estimate the distribution of A. With the RAPr formulation, extra information is then available to help the site owner understand how people use the site.6 More generally, the PageRank model has become a key tool for network and graph analysis. It has been used to find graph cuts [Andersen et al., 2006], infer missing values on a partially labeled graph [Zhou et al., 2005], find interesting genes [Morrison et al., 2005], and help match graph structures in protein networks [Singh et al., 2007].7 In all of these cases, the random surfer model does not directly apply. Each paper picks a particular value for α and computes a PageRank vector from that value. With RAPr, each case will have a natural random variable. For most, it may be a uniform distribution. Rather than reporting just a single number, the algorithms could use the standard deviation as natural error bounds representing uncertainty or sensitivity in the resulting PageRank vector. The sensitivity using the standard deviation accounts for fluctuations in the function over a wider interval than the derivative. 4.3 related work Our ideas have strong relationships with a few other classes of literature. Before delving into the details of the RAPr model, we’d like to discuss these relationships. 4.3.1 Teleportation parameters in literature Algorithmic papers on PageRank tend to investigate the behavior of Page- Rank algorithms for multiple values of α [Kamvar et al., 2003; Golub and Greif, 2006], whereas evaluations of the PageRank vector tend to use the canonical value α = 0.85 [Najork et al., 2007]. 5 There is already a paper on using a closely related idea for spam detection. See section 4.3.5. 6 One of the most useful obser- vations from this model is when people use the site in a way that is not predicted by the random surfer model with fitted parameters. This indicates that random surfer mod- els are not appropriate and could suggest monitoring a different set of statistics. 7 See section 1.4 for an informal description of these topics.PDF Image | Instagram Cheat Sheet
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