Clustering under Perturbation Resilience
نویسندگان
چکیده
منابع مشابه
Clustering under Perturbation Resilience
Motivated by the fact that distances between data points in many real-world clustering instances are often based on heuristic measures, Bilu and Linial [6] proposed analyzing objective based clustering problems under the assumption that the optimum clustering to the objective is preserved under small multiplicative perturbations to distances between points. In this paper, we provide several res...
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The k-center problem is a canonical and long-studied facility location and clustering problem with many applications in both its symmetric and asymmetric forms. Both versions of the problem have tight approximation factors on worst case instances: a 2-approximation for symmetric kcenter and an O(log*(k))-approximation for the asymmetric version. Therefore to improve on these ratios, one must go...
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Clustering under most popular objective functions is NP-hard, even to approximate well, and so unlikely to be efficiently solvable in the worst case. Recently, Bilu and Linial [11] suggested an approach aimed at bypassing this computational barrier by using properties of instances one might hope to hold in practice. In particular, they argue that instances in practice should be stable to small ...
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We study the notion of perturbation resilience introduced by Bilu and Linial (2010) and Awasthi, Blum, and Sheffet (2012). A clustering problem is α-perturbation resilient if the optimal clustering does not change when we perturb all distances by a factor of at most α. We consider a class of clustering problems with center-based objectives, which includes such problems as k-means, k-median, and...
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Iterative algorithms aimed at solving some problems are discussed. For certain problems, such as finding a common point in the intersection of a finite number of convex sets, there often exist iterative algorithms that impose very little demand on computer resources. For other problems, such as finding that point in the intersection at which the value of a given function is optimal, algorithms ...
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ژورنال
عنوان ژورنال: SIAM Journal on Computing
سال: 2016
ISSN: 0097-5397,1095-7111
DOI: 10.1137/140981575