cs345-streams2

cs345-streams2 - MoreStreamMining ComputingMoments 1 x...

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1 More Stream-Mining Counting How Many Elements Computing “Moments”
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2 Counting Distinct Elements Problem : a data stream consists of  elements chosen from a set of size  n .   Maintain a count of the number of  distinct elements seen so far. Obvious approach : maintain the set of  elements seen.
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3 Applications How many different words are found  among the Web pages being crawled at  a site? Unusually low or high numbers could  indicate artificial pages (spam?). How many different Web pages does  each customer request in a week?
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4 Using Small Storage Real Problem : what if we do not have  space to store the complete set? Estimate the count in an unbiased way. Accept that the count may be in error,  but limit the probability that the error is  large.
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5 Flajolet-Martin* Approach Pick a hash function  h   that maps each of  the  n  elements to log 2 n   bits, uniformly. Important that the hash function be (almost) a  random permutation of the elements. For each stream element  a , let  r  ( a  ) be  the number of trailing 0’s in  ( ).
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