Summary Conclusions: Computation of Minimum Volume Covering Ellipsoids*
Name
HPCES019.pdf
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187.7 KB
Format
Adobe PDF
Checksum (MD5)
b9e039a1f86d807561de500fdd71f601
Author(s)
Sun, Peng
Freund, Robert M.
Date Issued
January 2004
Series/Report no.
High Performance Computation for Engineered Systems (HPCES);
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.
Subjects
ellipsoid
Newton’s method
interior-point method
barrier method
active set
semidefinite program
data mining
robust statistics
clustering analysis
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