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Unformatted text preview: 1 Stream Clustering Extension of DGIM to More Complex Problems 2 Clustering a Stream r Assume points enter in a stream. r Maintain a sliding window of points. r Queries ask for clusters of points within some suffix of the window. r Important issue : where are the cluster centroids? 3 BDMO Approach r BDMO = Babcock, Datar, Motwani, OCallaghan. r k means based. r Can use less than O( N ) space for windows of size . r Generalizes trick of DGIM: buckets of increasing weight. 4 Recall DGIM r Maintains a sequence of buckets B 1 , B 2 , r Buckets have timestamps (most recent stream element in bucket). r Sizes of buckets nondecreasing. R In DGIM size = power of 2. r Either 1 or 2 of each size. 5 Alternative Combining Rule r Instead of combine the 2 nd and 3 rd of any one size we could say: r Combine B i+1 and B i if size(B i+1 B i ) < size(B i1 B i2 B 1 ). R If B i+1 , B i , and B i1 are the same size, inequality must hold (almost). R If B i1 is smaller, it cannot hold. 6 Buckets for Clustering r In place of size (number of 1s) we use (an approximation to) the sum of the distances from all points to the centroid of their cluster. centroid of their cluster....
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This document was uploaded on 03/04/2012.
 Fall '09

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