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142
Dynamic Coresets
, 2008
"... Abstract We give a dynamic data structure that can maintain an "coreset of n points, with respect to the extent measure, in O(log n) time for any constant " ? 0 and any constant dimension. The previous method by Agarwal, HarPeled, and Varadarajan requires polylogarithmic update t ..."
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approximate kcenters in O(minflog n; log log U g) randomized amortized time for any constant k and any constant dimension. For the smallest enclosing cylinder problem, we also show that a constantfactor approximation can be maintained in O(1) randomized amortized time on the word RAM.
Streaming Algorithms for kCenter Clustering with Outliers and with Anonymity
"... Abstract. Clustering is a common problem in the analysis of large data sets. Streaming algorithms, which make a single pass over the data set using small working memory and produce a clustering comparable in cost to the optimal offline solution, are especially useful. We develop the first streaming ..."
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Cited by 11 (0 self)
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algorithms achieving a constantfactor approximation to the cluster radius for two variations of the kcenter clustering problem. We give a streaming (4+ɛ)approximation algorithm using O(ɛ −1 kz) memory for the problem with outliers, in which the clustering is allowed to drop up to z of the input points
An Efficient Implementation of the Robust kCenter Clustering Problem
, 2010
"... The standard kcenter clustering problem is very sensitive to outliers. Charikar et al. proposed an alternative algorithm to cluster p points out of n total, thereby avoiding the distortion caused by outliers. The algorithm has an approximation bound of three times the true solution, but is very slo ..."
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The standard kcenter clustering problem is very sensitive to outliers. Charikar et al. proposed an alternative algorithm to cluster p points out of n total, thereby avoiding the distortion caused by outliers. The algorithm has an approximation bound of three times the true solution, but is very
Coresets for Polytope Distance
, 2009
"... Following recent work of Clarkson, we translate the coreset framework to the problems of finding the point closest to the origin inside a polytope, finding the shortest distance between two polytopes, Perceptrons, and soft as well as hardmargin Support Vector Machines (SVM). We prove asymptoticall ..."
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Cited by 14 (4 self)
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Following recent work of Clarkson, we translate the coreset framework to the problems of finding the point closest to the origin inside a polytope, finding the shortest distance between two polytopes, Perceptrons, and soft as well as hardmargin Support Vector Machines (SVM). We prove
Projective Clustering in High Dimensions using CoreSets
, 2002
"... Let P be a set of n points in IRd, and for any integer 0 < = k < = d 1, let RDk(P) denote the minimum over all kflats F of maxp2P dist(p, F). We present an algorithm that computes, for any 0 < " < 1, a kflat that is within a distance of (1 + ")RDk(P) from each point ..."
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Cited by 39 (9 self)
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Let P be a set of n points in IRd, and for any integer 0 < = k < = d 1, let RDk(P) denote the minimum over all kflats F of maxp2P dist(p, F). We present an algorithm that computes, for any 0 < " < 1, a kflat that is within a distance of (1 + ")RDk(P) from each point
Robust shape fitting via peeling and grating coresets
 In Proc. 17th ACMSIAM Sympos. Discrete Algorithms
, 2006
"... Let P be a set of n points in R d. A subset S of P is called a (k, ε)kernel if for every direction, the direction width of S εapproximates that of P, when k “outliers ” can be ignored in that direction. We show that a (k, ε)kernel of P of size O(k/ε (d−1)/2) can be computed in time O(n+k 2 /ε d−1 ..."
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Cited by 16 (3 self)
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−1). The new algorithm works by repeatedly “peeling” away (0, ε)kernels from the point set. We also present a simple εapproximation algorithm for fitting various shapes through a set of points with at most k outliers. The algorithm is incremental and works by repeatedly “grating ” critical points
Sublinear Projective Clustering with Outliers
"... Given a set of n points in ℜ d, a family of shapes S and a number of clusters k, the projective clustering problem is to find a collection of k shapes in S such that the maximum distance from a point to its nearest shape is minimized. Some special cases of the problem include the kline center probl ..."
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Cited by 1 (0 self)
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Given a set of n points in ℜ d, a family of shapes S and a number of clusters k, the projective clustering problem is to find a collection of k shapes in S such that the maximum distance from a point to its nearest shape is minimized. Some special cases of the problem include the kline center
Results 1  10
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142