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Lie Group Methods for Optimization with Orthogonality Constraints

Identifieur interne : 000846 ( Main/Exploration ); précédent : 000845; suivant : 000847

Lie Group Methods for Optimization with Orthogonality Constraints

Auteurs : D. Plumbley [Royaume-Uni]

Source :

RBID : ISTEX:FE2C407982B78EAB754C83671C0DF725862957C5

Abstract

Abstract: Optimization of a cost function J(W) under an orthogonality constraint WW T =I is a common requirement for ICA methods. In this paper, we will review the use of Lie group methods to perform this constrained optimization. Instead of searching in the space of n× n matrices W, we will introduce the concept of the Lie group SO(n) of orthogonal matrices, and the corresponding Lie algebraso(n). Using so(n) for our coordinates, we can multiplicatively update W by a rotation matrix R so that W′=RW always remains orthogonal. Steepest descent and conjugate gradient algorithms can be used in this framework.


Url:
DOI: 10.1007/978-3-540-30110-3_157


Affiliations:


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Le document en format XML

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