S. Guha, N. Mishra, R. Motwani, and L. O'Callaghan. Clustering data streams. In IEEE Symposium on Foundations of Computer Science (FOCS'00), Redondo Beach, CA, 2000. Home/Search Document Details and Download
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Optimal Time Bounds for Approximate Clustering - Mettu, Plaxton (2002) (3 citations) (Correct)
....factor of optimal. Specifically, for the case of uniform weights, our successive sampling algorithm yields a (k log (n k) O(1) configuration with high probability in O(nmax k, log n ) time. In addition to this sampling result, our algorithms rely on an extraction technique due to Guha et al. [8] that uses a black box O(1) approximate k median algorithm to compute a (k, O(1) configuration from any (m, O(1) assignment. The black box algorithm that we use is the linear time deterministic online median algorithm of Mettu and Plaxton [15] In developing our randomized algorithm for the ....
....Thorup gives a sampling technique that also consists of a series of sampling steps but produces an (O( k log n) #) 2 #) configuration for any positive real # with 0 # 0.4, but is only guaranteed to succeed with probability 1 2. For the data stream model of computation, Guha et al. [8] give a single pass O(1) approximate algorithm for the k median problem that runs in O(nk) time and requires O(n ) space for a positive constant #. They also establish a lower bound of # nk) for deterministic O(1) approximate k median algorithms. Mishra et al. 16] show that in order to ....
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S. Guha, N. Mishra, R. Motwani, and L. O'Callaghan. Clustering data streams. In Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science, pages 359--366, November 2000.
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....distance from data points to their closest cluster centers. The assumptions taken by the classical k median approach are: 17 1)each cluster can be e ectively modeled by a spherical Gaussian distribution, 2) each data item is assigned to one cluster and 3) the weights are assumed equal. In [50], a constant factor approximation algorithm for the k median problem is proposed which uses a single pass on the data stream model and requires workspace (n ) A related problem is the k center problem (minimize the maximum radius of a cluster) which is investigated in [30] where a single ....
....which uses a single pass on the data stream model and requires workspace (n ) A related problem is the k center problem (minimize the maximum radius of a cluster) which is investigated in [30] where a single pass algorithm which requires workspace O(k) is presented. In [75] results from [50] are used to develop an algorithm that achieves dramatically better clustering quality than BIRCH although it takes longer to run. In [16] a single pass algorithm is presented for points in the Euclidean space. The method used is based in identifying regions of the data that are compressible ....
S. Guha, N. Mishra, R. Motwani, and L. O'Callaghan. Clustering data streams. In FOCS, 2000.
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....factor of optimal. Specifically, for the case of uniform weights, our successive sampling algorithm yields a (k log (n=k) O(1) configuration with high probability in O(nmaxfk; log ng) time. In addition to this sampling result, our algorithms rely on an extraction technique due to Guha et al. [6] that uses a black box O(1) approximate k median algorithm to compute a (k, O(1) configuration from any (m, O(1) assignment. The black box algorithm that we use is the linear time deterministic online median algorithm of Mettu and Plaxton [12] In developing our randomized algorithm for the ....
....Thorup gives a sampling technique that also consists of a series of sampling steps but produces an (O( k log n) 2 ) configuration for any positive real with 0 0:4, but is only guaranteed to succeed with probability 1=2. For the data stream model of computation, Guha et al. [6] give a single pass O(1) approximate algorithm for the k median problem that runs in O(nk) time and requires O(n ) space for a positive constant . They also establish a lower bound of nk) for deterministic O(1) approximate k median algorithms. Mishra et al. 13] show that in order to ....
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S. Guha, N. Mishra, R. Motwani, and L. O'Callaghan. Clustering data streams. In Proceedings of the 41st Annual IEEE Symposium on Foundations of Computer Science, pages 359--366, November 2000.
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....A domain specific lan Figure 6: The precision and pruning power using dif guage, Hancock[6] has been designed at AT T to ferent numbers of coefficients, thresholds and datasets extract signatures from massive transaction streams. Algorithms for constructing decision trees[8] and clustering [15] for data streams have been proposed. ReTable 2: Precision after post processing cent work of Manku et al. 20] Greenwald et al. 14] Dataset R0.85 R0.85 R0.9 R0.9 S0.85 Tolerance 0.001 0.0005 0.001 0.0005 0.0005 Precision 0.9933 0.9947 0.9765 0.9865 0.9931 Recall 1.0 0.9995 1.0 0.9987 1.0 have ....
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S. Guha, N. Mishra, R. Motwani, and L. O'Callaghan. Clustering data streams. In Proc. 41st IEEE Symp. on Foundations of Computer Science, pages 359-366, Nov. 2000.
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