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A “vote” from an important page is worth more A page is important if it is pointed to by other important pages Define a “rank” r j for node j r j = ∑ i→ j r i d out (i) 2/7/2012 Jure Leskovec, <strong>Stanford</strong> C246: Mining Massive Datasets 6 a/2 a The web in 1839 a/2 y/2 y y/2 m Flow equations: ry = ry /2 + ra /2 ra = ry /2 + rm rm = ra /2 m
3 equations, 3 unknowns, no constants No unique solution All solutions equivalent modulo scale factor Additional constraint forces uniqueness y + a + m = 1 y = 2/5, a = 2/5, m = 1/5 Flow equations: ry = ry /2 + ra /2 ra = ry /2 + rm rm = ra /2 Gaussian elimination method works for small examples, but we need a better method for large web-size graphs 2/7/2012 Jure Leskovec, <strong>Stanford</strong> C246: Mining Massive Datasets 7
Page 1 and 2: CS246: Mining Massive Datasets Jure
Page 3 and 4: We will cover the following Link An
Page 5: Each link’s vote is proportional
Page 9 and 10: Suppose page j links to 3 pages, in
Page 11 and 12: y a m ry = ry /2 + ra /2 ra = ry /2
Page 13 and 14: Power Iteration: Set
Page 15 and 16: Where is the surfer at time t+1? F
Page 17 and 18: Example: a b ra 1 0 1 0 = rb 0 1 0
Page 19 and 20: 2 problems: Some pages are “dead
Page 21 and 22: The Google solution for spider trap
Page 23 and 24: Teleports: Follow random teleport l
Page 25 and 26: Theory of Markov chains Fact: For
Page 27 and 28: A chain is periodic if there exists
Page 29 and 30: Google’s solution that does it al
Page 31 and 32: a y a = m y 0.8·½+0.2·⅓ 1/3 1/
Page 33 and 34: Construct the N x N matrix A as fol
Page 35 and 36: Key step is matrix-vector multiplic
Page 37 and 38: Encode sparse matrix using only non
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

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