16-streams

322011 jure leskovec stanford c246 mining massive

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Unformatted text preview: t; 0 = not present Use DGIM to estimate counts of 1’s for all items 3/2/2011 Jure Leskovec, Stanford C246: Mining Massive Datasets 32 In principle, you could count frequent pairs or even larger sets the same way One stream per itemset Drawbacks: Only approximate Number of itemsets is way too big 3/2/2011 Jure Leskovec, Stanford C246: Mining Massive Datasets 33 Exponentially decaying windows: A heuristic for selecting likely frequent itemsets What are “currently” most popular movies? Instead of computing the raw count in last N elements Compute a smooth aggregation over the whole stream If stream is a1, a2,… and we are taking the sum of the stream, take the answer at time t to be: =Σi = 1,2,…,t ai e -c (t-i) (or, Σi = 1,…,t ai (1-c)t-i ) c is a constant, presumably tiny, like 10-6 or 10-9 3/2/2011 Jure Leskovec, Stanford C246: Mining Massive Datasets 34 If each ai is an “item” we can compute the characteristic function of each possible item x as an E.D.W. That is: Σi = 1,2,…,t δi e -c (t-i) where δi = 1 if ai = x, and 0 otherwise Call this sum the “weight” item x 3/2/2011 Jure Leskovec, Stanford C246: Mining Massive Datasets 35 ... 1/c 3/2/2011 Jure Leskovec, Stanford C246: Mining Massive Datasets 36 Suppose we want to find those items of weight at least ½ Important property: Sum over all weights is 1/(1 – e-c ) or very close to 1/[1 – (1 – c)] = 1/c Thus: At most 2/c items have weight at least ½. 3/2/2011 Jure Leskovec, Stanford C246: Mining Massive Datasets 37 Count (some) itemsets in an E.D.W. When a basket B comes in: 1. Multiply all counts by (1-c ); 2. For uncounted items in B, create new count. 3. Add 1 to count of any item in B and to any counted itemset contained in B. 4. Drop counts < ½. 5. Initiate new counts (next slide). * Informal proposal of Art Owen 3/2/2011 Jure Leskovec, Stanford C246: Mining Massive Datasets 38 Start a count for an itemset S ⊆ B if every proper subset of S had a count prior to arrival of basket B Example: Start counting {i, j} iff both i and j were counted prior to seeing B Example: Start counting {i, j, k} iff {i, j}, {i, k}, and {j, k} were all counted prior to seeing B 3/2/2011 Jure Leskovec, Stanford C246: Mining Massive Datasets 39 Counts for single items < (2/c) times the average number of items in a basket Counts for larger itemsets = ??. But we are conservative about starting counts of large sets. If we counted every set we saw, one basket of 20 items would initiate 1M counts. 3/2/2011 Jure Leskovec, Stanford C246: Mining Massive Datasets 40...
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This document was uploaded on 02/26/2014 for the course CS 246 at Stanford.

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