منابع مشابه
Chapter 17 Approximating a Convex Body by An Ellipsoid
In the following, we cover some material from linear algebra. Proofs of those facts can be found in any text on linear algebra, for example [Leo98]. For a matrix A, let A T denote the transposed matrix. We remind the reader that for two matrices A and B, we have (AB) T = B T A T. Furthermore, for any three matrices A, B and C, we have (AB)C = A(BC). A matrix A ∈ IR n×n is symmetric if A T = A. ...
متن کاملChapter 21 Approximating a Convex Body by An Ellipsoid
x " Is there anything in the Geneva Convention about the rules of war in peacetime? " Stalnko wanted to know, crawling back toward the truck. " Absolutely nothing, " Caulec assured him. " The rules of war apply only in wartime. In peacetime, anything goes. " – Gasp, Romain Gary. In this chapter, we show that any convex body can be approximated " reasonably well " by an ellipsoid. (A quick remin...
متن کاملApproximating the Covariance Matrix with Low-rank Perturbations
Covariance matrices capture correlations that are invaluable in modeling real-life datasets. Using all d elements of the covariance (in d dimensions) is costly and could result in over-fitting; and the simple diagonal approximation can be over-restrictive. We present an algorithm that improves upon the diagonal matrix by allowing a low rank perturbation. The efficiency is comparable to the diag...
متن کاملApproximating the Covariance Matrix of GMMs with Low-Rank Perturbations
Covariance matrices capture correlations that are invaluable in modeling real-life datasets. Using all d elements of the covariance (in d dimensions) is costly and could result in over-fitting; and the simple diagonal approximation can be over-restrictive. In this work, we present a new model, the Low-Rank Gaussian Mixture Model (LRGMM), for modeling data which can be extended to identifying pa...
متن کاملOn the Equivalence of the General Covariance Union (GCU) and Minimum Enclosing Ellipsoid (MEE) Problems
In this paper we describe General Covariance Union (GCU) and show that solutions to GCU and the Minimum Enclosing Ellipsoid (MEE) problems are equivalent. This is a surprising result because GCU is defined over positive semidefinite (PSD) matrices with statistical interpretations while MEE involves PSD matrices with geometric interpretations. Their equivalence establishes an intersection betwee...
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ژورنال
عنوان ژورنال: Communications in Contemporary Mathematics
سال: 2020
ISSN: 0219-1997,1793-6683
DOI: 10.1142/s0219199719500895