Computation of minimum-volume covering ellipsoids

Computation of minimum-volume covering ellipsoids

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Article ID: iaor20073867
Country: United States
Volume: 52
Issue: 5
Start Page Number: 690
End Page Number: 706
Publication Date: Sep 2004
Journal: Operations Research
Authors: ,
Keywords: datamining, matrices, statistics: multivariate
Abstract:

We present a practical algorithm for computing the minimum-volume n-dimensional ellipsoid that must contain m given points a1,…,am ∈ ℜn. 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 much theoretical complexity analysis. Here we focus on computation. We present a combined interior-point and active-set method for solving this problem. Our computational results demonstrate that our method solves very large problem instances (m = 30,000 and n = 30) to a high degree of accuracy in under 30 seconds on a personal computer.

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