منابع مشابه
Minimum 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 ...
متن کاملScale-invariant clustering with minimum volume ellipsoids
This paper develops theory and algorithms concerning a new metric for clustering data. The metric minimizes the total volume of clusters, where the volume of a cluster is defined as the volume of the minimum volume ellipsoid (MVE) enclosing all data points in the cluster. This metric is scale-invariant, that is, the optimal clusters are invariant under an affine transformation of the data space...
متن کاملMinimum 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 ...
متن کاملMinimum-Volume Enclosing Ellipsoids and Core Sets1
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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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1964
ISSN: 0025-5718
DOI: 10.2307/2002957