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78 4 ⋅ random alpha pagerank This equation gives the direct relationship between a path damping equation andRAPr. IfwecanconstructAsuchthatP[L=l]=E[Al]−E[Al+1], then we could establish a direct relationship between the models. Thus, we need to match moments P [L = 0] = E [A0 ] − E [A1 ] P [L = 1] = E [A1 ] − E [A2 ] P [L = 2] = E [A2 ] − E [A3 ] E [A0 ] = 1 E [A1 ] = E [A0 ] − P [L = 0] ⇒ (4.19) E [A2 ] = E [A1 ] − P [L = 1] ⋮⋮ Computing such a distribution of A is a special case of the Hausdorff moment problem [Talenti, 1987], which has a known characterization for a unique solution. We go no further than noting this equivalence. 4.5 empirical distribution As we argued in the previous sections, the RAPr model generalizes Page- Rank to multiple random surfers. Instead of picking a value of α to control when the random surfer teleports, RAPr forces us to pick a distribution for a random variable A that controls how likely surfers are to pick a value of α. This second task seems more problematic. For a natural choice of A, it is not. This natural choice is to pick A according to how surfers actually behave on the web. Recall that a single value of α is the probability a user clicks a link on a web page. With a custom browser plug-in, you could compute your own value of α. It’s a simple ratio number of pages viewed after clicking a link α≈. total number of pages viewed With more browsing, and more information, the approximation to α grows more refined. If people tracked their own α, finding the empirical distribution for A would be just a matter of data collection. Loosely speaking, browser toolbars collect precisely this type of informa- tion. That is, the Microsoft, Yahoo!, and Google browser toolbars—which users download and install into their browsers for a few improvements— collect this data and send it back to Microsoft, Yahoo!, and Google. (Of course, each company ensures that users provide explicit consent for trans- mitting the data.) Toolbar logs, then, have the information to compute A.PDF Image | Instagram Cheat Sheet
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