Modified algorithms for the minimum volume enclosing axis-aligned ellipsoid problem

Computing 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 ...

Two Algorithms for the Minimum Enclosing Ball Problem

Given A := {a1, . . . , am} ⊂ Rn and > 0, we propose and analyze two algorithms for the problem of computing a (1 + )-approximation to the radius of the minimum enclosing ball of A. The first algorithm is closely related to the Frank-Wolfe algorithm with a proper initialization applied to the dual formulation of the minimum enclosing ball problem. We establish that this algorithm converges in O...

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.

Algorithms for minimum volume enclosing simplex in R3

The Minimum Volume Ellipsoid Metric

We propose an unsupervised “local learning” algorithm for learning a metric in the input space. Geometrically, for a given query point, the algorithm finds the minimum volume ellipsoid (MVE) covering its neighborhood which characterizes the correlations and variances of its neighborhood variables. Algebraically, the algorithm maximizes the determinant of the local covariance matrix which amount...