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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5.6 ⋅ numerical results 105 160 150 140 130 120 110 100 90 80 70 0 0.1 0.2 0.3 0.4 0.5 β 0.6 0.7 0.8 www, α=0.85 power η = 1e−01 η = 1e−02 η = 1e−03 η = 1e−04 η = 1e−05 160 150 140 130 120 110 100 90 80 70 60 0 0.1 0.2 0.3 0.4 0.5 0.6 β 0.7 0.8 in−2004, α=0.85 power η = 1e−01 η = 1e−02 η = 1e−03 η = 1e−04 η = 1e−05 160 150 140 130 120 110 100 90 80 70 −4 −3 −2 −1 10 10 10 10 η www, α=0.85 power β = 0.10 β = 0.30 β = 0.50 β = 0.70 160 150 140 130 120 110 100 90 80 70 −4 −3 −2 −1 10 10 10 10 η in−2004, α=0.85 power β = 0.10 β = 0.30 β = 0.50 β = 0.70 in−2004, α=0.99 in−2004, α=0.99 power η = 1e−01 η = 1e−02 η = 1e−03 η = 1e−04 η = 1e−05 1500 1500 power β = 0.10 β = 0.30 β = 0.50 β = 0.70 1400 1400 1300 1300 1200 1200 1100 1100 1000 1000 900 900 800 800 700 −4 −3 −2 −1 700 10 10 10 10 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 ηβ Figure 5.1 – Performance of the inner-outer iteration with varied β and η. We measure perfor- mance with matrix-vector products in this case. For the www and in-2004 graphs, we fix β and vary η in the left figures, and we fix η and vary β in the right figures. The top rows use α = 0.85 and the bottom row uses α = 0.99. This plot suggests that β = 0.5 and η = 10−2 is a good choice. The only graph that the inner-outer scheme does not accelerate with these parameters is the www graph with α = 0.85. Multiplications Multiplications Multiplications Multiplications Multiplications Multiplications

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