J. Kleinberg, C. H. Papadimitriou, P. Raghavan. "Segmentation problems," Proc. ACM Symposium on Theory of Computing, 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....for evaluating the results of data mining operations according to the utility of the results in decision making which is formalized as 21 an economically motivated optimization problem. This framework leads to interesting optimization problems such as the segmentation problem which is studied in [64]. Segmentation problems are related to clustering. 9 Conclusion We discussed formal methods used for developing algorithms suitable for data mining applications where data are read into main memory only once and a limited amount of storage space is available. Then we discussed problems that are ....

J. M. Kleinberg, C. H. Papadimitriou, and P. Raghavan. Segmentation problems. In STOC, pages 473-482, 1998. 24

.... the 2 Catalog Segmentation Problem Using Semide nite Programming Relaxations Dachuan Xu Yinyu Ye Jiawei Zhang May 6, 2002 Abstract We consider the 2 Catalog Segmentation problem (2 CSP) introduced by Kleinberg, Papadimitriou and Raghavan [10]. In this problem, we are given a ground set I of n items, a family fS 1 ; S 2 ; Sm g of subsets of I and an integer 1 k n. The objective is to nd subsets A 1 ; A 2 I such that jA 1 j = jA 2 j = k and P m i=1 maxfjS i A 1 j; jS i A 2 jg is maximized. It is known that a simple ....

....I of n items, a family fS 1 ; S 2 ; Sm g of subsets of I and an integer 1 k n. The objective is to nd subsets A 1 ; A 2 I such that jA 1 j = jA 2 j = k and P m i=1 maxfjS i A 1 j; jS i A 2 jg is maximized. It is known that a simple greedy algorithm has a performance guarantee 2 [10]. Furthermore, using an semide nite programming (SDP) relaxation Doids, Guruswami and Khanna [2] showed that 2 CSP can be approximated by a factor of 0:56 when k = n=2. On the negative side, Asodi and Safra [1] proved that a polynomial time ( 2 ) approximation algorithm, for any constant ....

[Article contains additional citation context not shown here]

J. Kleinberg, C. Papadimitriou, and P. Raghavan. Segmentation problems. In Proceedings of the 30th Symposium on Theory of Computation, pages 473-482, 1998.

....separations is polynomial in n, and we can check each of them eciently. However, the combinatorial complexity of the problem grows exponentially with the dimension. Indeed, the k clustering problem was shown to be NP hard even for k = 2 in several cases. Kleinberg, Papadimitriou, and Raghavan [34] show it for the binary cube, and Drineas, Frieze, Kannan, Vempala, and Vinay show it for R d with squared Euclidean distances. The NP hardness of the Euclidean distances case is still open. We note that in xed dimension, for arbitrary k, Arora, Raghavan, and Rao [6] give a polynomial time ....

J. Kleinberg, C. Papadimitriou, and P. Raghavan. Segmentation problems. In Proc. STOC '98.

....separations is polynomial in n, and we can check each of them efficiently. However, the combinatorial complexity of the problem grows exponentially with the dimension. Indeed, the k clustering problem was shown to be NP hard even for k = 2 in several cases. Kleinberg, Papadimitriou, and Raghavan [33] show it for the binary cube, and Drineas, Frieze, Kannan, Vempala, and Vinay show it for R d with squared Euclidean distances. The NP hardness of the Euclidean distances case is still open. We note that in fixed dimension, for arbitrary k, Arora, Raghavan, and Rao [6] give a polynomial time ....

J. Kleinberg, C. Papadimitriou, and P. Raghavan. Segmentation problems. In Proc. STOC '98.

....We study the 2 Catalog Segmentation problem: Given a set I of n items and a family S = fS 1 ; S 2 ; S p g of subsets of I, find C 1 ; C 2 I such that jC 1 j; jC 2 j r and the sum P p i=1 maxfjS i C 1 j; jS i C 2 jg is maximized. The problem was recently introduced by Kleinberg et al. [2] and is motivated by several applications to data mining and clustering operations as detailed in [2] Under the restriction that jS i j = Omega Gamma jIj) for each S i , the authors give a PTAS. But, in general, only a trivial 0.5approximation algorithm is known just define C 1 to be r most ....

....: S p g of subsets of I, find C 1 ; C 2 I such that jC 1 j; jC 2 j r and the sum P p i=1 maxfjS i C 1 j; jS i C 2 jg is maximized. The problem was recently introduced by Kleinberg et al. [2] and is motivated by several applications to data mining and clustering operations as detailed in [2]. Under the restriction that jS i j = Omega Gamma jIj) for each S i , the authors give a PTAS. But, in general, only a trivial 0.5approximation algorithm is known just define C 1 to be r most frequently occurring elements. The question of improving upon this factor was posed as an important ....

[Article contains additional citation context not shown here]

J. Kleinberg, C. Papadimitriou and P. Raghavan. Segmentation Problems. STOC 98, pp. 473-482.

No context found.

J. Kleinberg, C. H. Papadimitriou, P. Raghavan. "Segmentation problems," Proc. ACM Symposium on Theory of Computing, 1998.

....preference; indeed, we do not require the users to be drawn from one of a small number of types , as implicitly needed in [17] On the other hand, our algorithm does not achieve the strong document clustering results that [17] establishes for LSI. The final category includes segmentation [15] problems. This class is perhaps the most closely related because there is an explicit notion of value or utility. The segmentation model described in [15] however, is very general and does not seem to be analyzable in our context. Tractable special cases of the segmentation problem include ....

....our algorithm does not achieve the strong document clustering results that [17] establishes for LSI. The final category includes segmentation [15] problems. This class is perhaps the most closely related because there is an explicit notion of value or utility. The segmentation model described in [15], however, is very general and does not seem to be analyzable in our context. Tractable special cases of the segmentation problem include facility location [8] LSI, and clustering. In each of these cases, the data is embedded in an explicit metric or similarity space, which plays a central role ....

J. Kleinberg, C. H. Papadimitriou, and P. Raghavan. Segmentation problems. Proceedings of the ACM Symposium on Theory of Computing, 1998.

No context found.

J. Kleinberg, C. Papadimitriou, and P. Raghavan, Segmentation problems, in "Proc. of the 30th ACM STOC," pp. 473]482, Assoc. Comput. Mach., New York, 1998.

....market, adopting a set of policies to the segments they target. Building on the classical setting of game theory, we develop a notion of segmented matrix games to model this setting. This quickly leads to a number of novel (and largely unsolved) issues in computational game theory. In related work [13] in the area of discrete algorithms and complexity theory 4 , we have studied approximation algorithms for some of the most basic segmentation problems that arise from our framework. This leads to interesting connections with classical problems of combinatorial optimization such as facility ....

....with classical problems of combinatorial optimization such as facility location and the maximization of submodular functions and to settings in which one can concretely analyze the power of methods such as random sampling and greedy iterative improvement algorithms. We refer the reader to [13] for further details. 2 Three examples We pointed out above that aggregation is especially unsatisfactory and inaccurate when the cost function g(x; y i ) is nonlinear in y i . The next two anecdote based examples illustrate certain interesting and common kinds of nonlinearities. The third ....

[Article contains additional citation context not shown here]

J. Kleinberg, C. H. Papadimitriou, P. Raghavan. "Segmentation problems," Proc. ACM STOC, 1998.

No context found.

J. Kleinberg, C. Papadimitriou, and P. Raghavan. Segmentation problems. In Proc. STOC '98.

No context found.

J. Kleinberg, C. Papadimitriou, and P. Raghavan. Segmentation problems. J. ACM, 51(2):263--280, 2004.

No context found.

J. Kleinberg, C. Papadimitriou, and P. Raghavan. Segmentation problems. In Proceedings of the ACM Symposium on Theory of Computing, pages 473--482, 1998.

No context found.

J. Kleinberg, C. Papadimitriou, and P. Raghavan. Segmentation problems. In Proc. of the 30th Ann. ACM Symp. on Theory of Computing (STOC), 1998, pages 473-482.

No context found.

J. Kleinberg, C. Papadimitriou, and P. Raghavan. Segmentation problems. In Proc. of the 30th Ann. ACM Symp. on Theory of Computing, 1998, pages 473-482.

No context found.

J. Kleinberg, C. Papadimitriou, and P. Raghavan. Segmentation problems. In Proc. of the 30th Ann. ACM Symp. on Theory of Computing, 1998, pages 473--482.

No context found.

J. Kleinberg, C. Papadimitriou, and P. Raghavan. Segmentation problems. In Proc. of the 30th Ann. ACM Symp. on Theory of Computing (STOC), 1998, pages 473--482.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC