Jure Leskovec, Stanford University - SNAP - Stanford University

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1 3 7 6 2 5 4 4 2 1 3 6 7 5 3 4 7 6 1 2 5 1 1 0 0 0 1 1 Input matrix 0 0 1 1 1 0 0 3/9/2011 Jure Leskovec, Stanford C246: Mining Massive Datasets 1 0 0 0 0 1 1 0 1 1 1 1 0 0 Signature matrix M 2 2 1 1 1 2 Similarities: 1-3 2-4 1-2 3-4 Col/Col 0.75 0.75 0 0 Sig/Sig 0.67 1.00 0 0 2 4 1 1 1 2 10
ands Hash cols of signature matrix M: Similar columns likely hash to same bucket Cols. x and y are a candidate pair if M (i, x) = M (i, y) for at least frac. s values of i Divide matrix M into b bands of r rows r rows Buckets Matrix M Prob. of sharing a bucket Sim(C 1 ,C 2)=s Prob. that at least 1 band is identical = 1 - (1 - s r ) b Given s, tune r and b to get almost all pairs with similar signatures, but eliminate most pairs that do not have similar signatures Sim. threshold s b=20, r=5 s 1-(1-s r ) b .2 .006 .3 .047 .4 .186 .5 .470 .6 .802 .7 .975 .8 .9996 3/9/2011 Jure Leskovec, Stanford C246: Mining Massive Datasets 11 2 1 2 1 2 1 4 1 2 1 2 1
Page 1 and 2: CS246: Mining Massive Datasets Jure
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Jure Leskovec, Stanford University - SNAP - Stanford University

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