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34 2 ⋅ pagerank background The solution of w(α)T also resolves our second concern, the eT V−1 factor in +(α)T . After partitioning we have 1 and the latter, The relationship is P = ST , so that X0 =Z0T andY0 =V0T. ⎡⎢ Z 0 ⎤⎥ V−1 = ⎢Z ⎥ ⎢Z1 ⎥ ⎣ 2⎦ (2.45) +(α)T = vTV Z +(1−α)vTV (I−αD )−1Z +(1−α)vTV (I−αJ )−1Z , 00111222 (2.46) whichisvalidforall0≤α≤1andactuallyallαotherthanthesetα= 1 λi where λi is an eigenvalue of S and λi =/ 0. checking back Fromthelinearsystem,wefoundthatx(1)=X0Y0v and from the eigensystem, we found +(1)T = vT V0 Z0 . In the former, I Y0 P=[X0 X1 X2 ][ D1 ][Y1 ], I Z0 S=[V0 V1 V2 ][ D1 ][Z1 J2 Z2 Thus we find the same limit vectors in each formulation. 2.8 pagerank datasets Most of this chapter has discussed the theory of PageRank. But a large portion of this thesis involves actually computing PageRank. Thus, we need data to compute PageRank, and in this case: bigger really is better. Table 2.2 shows a series of properties for the datasets used in the forthcoming exper- iments. Each dataset is a directed graph G = (V,E). I either collected the dataset myself or took it from a publicly available source. The graphs aa-stan, ee-stan, and cs-stan correspond to the web graphs for the hosts aa.stanford.edu, ee.stanford.edu, and cs.stanford.edu, respectively. These graphs were formed as a subset of the Webbase 2001 crawl [Hirai et al., 2000] compressed with the Webgraph framework [Boldi and Vigna, 2005]. The graph cnr-2000 is the result of an Ubicrawler crawl [Boldi et al., 2004]. J2 Y2 ].PDF Image | ALGORITHMS FOR PAGERANK SENSITIVITY DISSERTATION
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