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concrete meaning. For a protein matching problem, it is observed experimen- tally in Singh et al. [2007] that values of α between 0.7 and 0.95 yield good results. We look at a case when A is the 2-core of the undirected graph of subject headings from the Library of Congress [Various, 2008] (abbreviated LCSH-2) and B is the 3-core of the undirected Wikipedia category structure [Various, 2007] (abbreviated WC-3). We previously used these datasets in analyzing the actual matches in a slightly different setting [Bayati et al., 2009]. The size of these datasets is reported in table 5.5. For this application, the weights come from a text-matching procedure on the labels of the two graphs. 5.6 ⋅ numerical results 113 dataset LCSH-2 WC-3 Product Graph size 59,849 70,509 4,219,893,141 non-zeros 227,464 403,960 91,886,357,440 Table 5.5 – IsoRank datasets. In this experiment, we do not investigate all the issues involved in using a heuristic to an NP-hard problem and focus on the performance of the inner-outer algorithm in a non-Web ranking context. Without any parameter optimization (i.e., using β = 0.5 and η = 10−2 ), the inner-outer scheme shows a significant performance advantage as demonstrated in table 5.6. Inner-Outer Power 188 mat-vec 271 mat-vec 36.2 hours 54.6 hours Table 5.6 – Inner-Outer performance for IsoRank. The inner-outer iteration (β = 0.5, η = 10−2) is also faster than the power method on IsoRank with α = 0.95, τ = 10−7, and v sparse and non-uniform. The computations were done in pure Matlab and the product graph is never explicitly formed.PDF Image | MODELS AND ALGORITHMS FOR PAGERANK SENSITIVITY
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