منابع مشابه
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...
متن کاملOn the Minimum Volume Covering Ellipsoid of Ellipsoids
We study the problem of computing a (1+ )-approximation to the minimum volume covering ellipsoid of a given set S of the convex hull of m full-dimensional ellipsoids in Rn. We extend the first-order algorithm of Kumar and Yıldırım that computes an approximation to the minimum volume covering ellipsoid of a finite set of points in Rn, which, in turn, is a modification of Khachiyan’s algorithm. F...
متن کاملOn the Minimum Volume Covering Ellipsoid of Ellipsoids
Let S denote the convex hull of m full-dimensional ellipsoids in Rn. Given > 0 and δ > 0, we study the problems of computing a (1 + )-approximation to the minimum volume covering ellipsoid of S and a (1 + δ)n-rounding of S. We extend the first-order algorithm of Kumar and Yıldırım that computes an approximation to the minimum volume covering ellipsoid of a finite set of points in Rn, which, in ...
متن کاملLocation adjustment for the minimum volume ellipsoid estimator
Estimating multivariate location and scatter with both affine equivariance and positive breakdown has always been difficult. A well-known estimator which satisfies both properties is the Minimum Volume Ellipsoid Estimator (MVE). Computing the exact MVE is often not feasible, so one usually resorts to an approximate algorithm. In the regression setup, algorithms for positive-breakdown estimators...
متن کاملThe Minimum Volume Covering Ellipsoid Estimation in Kernel-Defined Feature Spaces
Minimum volume covering ellipsoid estimation is important in areas such as systems identification, control, video tracking, sensor management, and novelty detection. It is well known that finding the minimum volume covering ellipsoid (MVCE) reduces to a convex optimisation problem. We propose a regularised version of the MVCE problem, and derive its dual formulation. This makes it possible to a...
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ژورنال
عنوان ژورنال: Wiley Interdisciplinary Reviews: Computational Statistics
سال: 2009
ISSN: 1939-5108,1939-0068
DOI: 10.1002/wics.19