MODELS AND ALGORITHMS FOR PAGERANK SENSITIVITY

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

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2 1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 Figure 4.6 – Empirically measured tele- portationcoefcients. Fortwohoursof toolbar logs, the black histogram repre- sents the raw values of α recorded. The dashed line is a bounded kernel density fit to the data with a kernel width of 0.1. The blue line is a Beta density ap- proximation to α. In the original data, rational values of α with small denomi- nators are likely—and cause spikes in the histogram—because many individuals are only briefly observed. 4.5 ⋅ empirical distribution 71 Histogram Density Fit Beta(1.5,0.5) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 α problem when the only observation of a person are page views with no clicks. The α is 0, which is incorrect. By assumption, everyone will click on a link at some point and the pseudo-counts adjust for these finite size results. Two aspects of the Beta fit are surprising. First, web surfers do not often click links! The “mean” user clicks a link once for every three pages. Such behavior may suggest that search and bookmarks are the prevalent means of navigating the web. Second, the distribution and its fits extend to α = 1. In all the nonlinear least squares variations, the right endpoint of each fit was 1. Thus, long browsing sessions are common on the web. In closing, we repeat that A can be measured from data, and A ∼ Beta(1.5, 0.5, [0, 1]) is a reasonable approximation. While this analysis is preliminary, it supports a few surprising observations about random surfer browsing on the web. density

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