Minimum-Volume Enclosing Ellipsoids and Core Sets
نویسندگان
چکیده
منابع مشابه
Minimum Volume Enclosing Ellipsoids and Core Sets
Abstract. We study the problem of computing a (1 + )-approximation to the minimum volume enclosing ellipsoid of a given point set S = {p1, p2, . . . , pn} ⊆ Rd. Based on a simple, initial volume approximation method, we propose a modification of Khachiyan’s first-order algorithm. Our analysis leads to a slightly improved complexity bound of O(nd3/ ) operations for ∈ (0, 1). As a byproduct, our ...
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We study the problem of computing the minimum volume enclosing ellipsoid containing a given point set S = {p1, p2, . . . , pn} ⊆ R. Using “core sets” and a column generation approach, we develop a (1 + )-approximation algorithm. We prove the existence of a core set X ⊆ S of size at most |X| = α = O ( d ( log d + 1 )) . We describe an algorithm that computes the set X and a (1 + )-approximation ...
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We study the problem of computing a (1 + )-approximation to the minimum volume enclosing ellipsoid of a given point set S = {p, p, . . . , p} ⊆ R. Based on a simple, initial volume approximation method, we propose a modification of Khachiyan’s first-order algorithm. Our analysis leads to a slightly improved complexity bound of O(nd/ ) operations for ∈ (0, 1). As a byproduct, our algorithm retur...
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Two different methods for computing the covering ellipses of a set of points are presented. The first method finds the optimal ellipsoids with the minimum volume. The second method uses the first and second moments of the data points to compute the parameters of an ellipsoid that covers most of the points. A MATLAB software is written to verify the results.
متن کاملComputing Minimum-Volume Enclosing Axis-Aligned Ellipsoids
Given a set of points S = {x1, . . . , xm} ⊂ R and > 0, we propose and analyze an algorithm for the problem of computing a (1 + )-approximation to the minimum-volume axis-aligned ellipsoid enclosing S . We establish that our algorithm is polynomial for fixed . In addition, the algorithm returns a small core set X ⊆ S , whose size is independent of the number of points m, with the property that ...
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ژورنال
عنوان ژورنال: Journal of Optimization Theory and Applications
سال: 2005
ISSN: 0022-3239,1573-2878
DOI: 10.1007/s10957-005-2653-6