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مقاله‌ی دسترسی آزاد

Computing minimum-volume enclosing ellipsoids

['Nathaniel Bowman', 'Michael T. Heath', '']

چکیده

Abstract For a given multidimensional data set (point cloud), we investigate methods for computing the minimum-volume enclosing ellipsoid (MVEE), which provides an efficient representation of that is useful in many applications, including analysis, optimal design, and computational geometry. Contrary to conventional wisdom, demonstrate careful exploitation problem structure can enable high-order (Newton Newton-like) with superlinear convergence rates scale very large MVEE problems. We also introduce hybrid method combines benefits both low-order methods, along new initialization schemes further enhance performance. Observing cost depends significantly on particular distribution data, kurtosis serves as excellent indicator difficulty guidance choosing appropriate solution algorithm initialization.

اسناد مشابه

  • Linear convergence of a modified Frank-Wolfe algorithm for computing minimum-volume enclosing ellipsoids

    سند علمی۲۰۰۸Optimization Methods and SoftwareSelin Damla Ahipasaoglu, Peng Sun, Michael J. Todd

    We show the linear convergence of a simple first-order algorithm for the minimum-volume enclosing ellipsoid problem and its dual, the D-optimal design problem of statistics. Computational tests confirm the attractive features of this method.

  • Linear convergence of a modified Frank–Wolfe algorithm for computing minimum-volume enclosing ellipsoids

    مقاله‌ی دسترسی آزاد۲۰۰۸Optimization Methods and SoftwareS.Damla Ahipasaoglu, PengSun, Michael J.Todd

  • On Khachiyan's algorithm for the computation of minimum-volume enclosing ellipsoids

    سند علمی۲۰۰۷Discrete Applied MathematicsMichael J. Todd, E. Alper Yildirim

    Given A := {a1, . . . , am} ⊂ Rd whose affine hull is Rd, we study the problems of computing an approximate rounding of the convex hull of A and an approximation to the minimum volume enclosing ellipsoid of A. In the case of centrally symmetric sets, we first establish that Khach

  • Computing Minimum-Volume Enclosing Axis-Aligned Ellipsoids

    سند علمی۲۰۰۶P. Kumar, E. A. Yıldırım

    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 al

  • Approximate Minimum Volume Enclosing Ellipsoids Using Core Sets

    سند علمی۲۰۰۳Piyush Kumar, E. Alper Yıldırım

    We study the problem of computing the minimum volume enclosing ellipsoid containing a given point set S = {p1, p2, . . . , pn} ⊆ R. Using “core sets” and a column generation approach, we develop a (1 + )-approximation algorithm. We prove the existence of a core set X ⊆ S of size

  • Minimum Volume Enclosing Ellipsoids and Core Sets

    سند علمی۲۰۰۴Piyush Kumar, E. Alper Yıldırım

    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.