r - SNAP - Stanford University

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Imagine a random web surfer: At any time t, surfer is on some page u At time t+1, the surfer follows an out-link from u uniformly at random Ends up on some page v linked from u Process repeats indefinitely Let: p(t) … vector whose i th coordinate is the prob. that the surfer is at page i at time t p(t) is a probability distribution over pages 2/7/2012 Jure Leskovec, <strong>Stanford</strong> C246: Mining Massive Datasets 14 r j i 1 i 2 i 3 = j ∑ i→ j dout ri (i)
Where is the surfer at time t+1? Follows a link uniformly at random p(t+1) = M · p(t) Suppose the random walk reaches a state p(t+1) = M · p(t) = p(t) then p(t) is stationary distribution of a random walk Our rank vector r satisfies r = M · r So, it is a stationary distribution for the random walk i 1 i 2 i 3 p( t + 1) = M ⋅ p( t) 2/7/2012 Jure Leskovec, <strong>Stanford</strong> C246: Mining Massive Datasets 15 j
Page 1 and 2: CS246: Mining Massive Datasets Jure
Page 3 and 4: We will cover the following Link An
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Page 11 and 12: y a m ry = ry /2 + ra /2 ra = ry /2
Page 13: Power Iteration: Set
Page 17 and 18: Example: a b ra 1 0 1 0 = rb 0 1 0
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Page 33 and 34: Construct the N x N matrix A as fol
Page 35 and 36: Key step is matrix-vector multiplic
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Page 39 and 40: Assume enough RAM to fit r new into
Page 41 and 42: Similar to nested-loop join in data
Page 43 and 44: Break M into stripes Each stripe c

r - SNAP - Stanford University

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