cs345-streams4

cs345-streams4 - Stream Clustering Extension of DGIM to...

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