Computation of Minimum Volume Covering Ellipsoids
نویسندگان
چکیده
منابع مشابه
Computation of Minimum-Volume Covering Ellipsoids
We present a practical algorithm for computing the minimum volume n-dimensional ellipsoid that must contain m given points a1, . . . , am ∈ R. This convex constrained problem arises in a variety of applied computational settings, particularly in data mining and robust statistics. Its structure makes it particularly amenable to solution by interior-point methods, and it has been the subject of m...
متن کاملOn the Minimum Volume Covering Ellipsoid of Ellipsoids
Let S denote the convex hull of m full-dimensional ellipsoids in Rn. Given > 0 and δ > 0, we study the problems of computing a (1 + )-approximation to the minimum volume covering ellipsoid of S and a (1 + δ)n-rounding of S. We extend the first-order algorithm of Kumar and Yıldırım that computes an approximation to the minimum volume covering ellipsoid of a finite set of points in Rn, which, in ...
متن کاملOn the Minimum Volume Covering Ellipsoid of Ellipsoids
We study the problem of computing a (1+ )-approximation to the minimum volume covering ellipsoid of a given set S of the convex hull of m full-dimensional ellipsoids in Rn. We extend the first-order algorithm of Kumar and Yıldırım that computes an approximation to the minimum volume covering ellipsoid of a finite set of points in Rn, which, in turn, is a modification of Khachiyan’s algorithm. F...
متن کاملMinimum Volume Enclosing Ellipsoids
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: SSRN Electronic Journal
سال: 2002
ISSN: 1556-5068
DOI: 10.2139/ssrn.321262