Modeling of creative thinking

Extreme ellipsoids as approximations of design space in data predictive metamodeling problems

A. A. Bedrintsev^a, V. V. Chepyzhov^a, S. S. Chernova<sup>b

a</sup> Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
^b Institute for Systems Analysis of Russian Academy of Sciences

Abstract: This paper proposes an approach to obtaining of the set of admissible values of the optimization variables (design space) in the form of extreme ellipsoids describing a given set of points and inscribed in a given set of linear constraints. Considered ellipsoids include Principal Component’s ellipsoid, minimal volume ellipsoid and ellipsoid with minimal trace of its matrix containing given points. We have developed the procedures which change ellipsoid built based on points set exclusively in order to inscribe it into polyhedron. Ellipsoids are constructed by solving corresponding optimization problems which are formulated as convex programming problems using linear matrix inequalities.

Keywords: data representation; extreme ellipsoids; convex optimization; linear matrix inequalities; Principal Components Analysis.

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