MVEE
MVEE stands for minimum volume enclosing ellipsoid. It is the smallest ellipsoid that contains a given set of points in real space and is a common tool in data analysis and geometry. For a finite set of points x_i in R^d, the MVEE finds a center c in R^d and a positive definite matrix A in R^{d×d} such that the ellipsoid E = { x : (x − c)^T A (x − c) ≤ 1 } contains all the points and its volume is minimized. The volume of such an ellipsoid is proportional to det(A)^{-1/2}, so the optimization seeks to maximize det(A) subject to the containment constraints.
The problem is convex and can be formulated as a semidefinite program. A widely used practical approach
Applications of the MVEE include robust data normalization, outlier detection, pattern recognition, and preprocessing in machine