Lie Group Methods for Optimization with Orthogonality Constraints
Identifieur interne : 001030 ( Main/Curation ); précédent : 001029; suivant : 001031Lie Group Methods for Optimization with Orthogonality Constraints
Auteurs : D. Plumbley [Royaume-Uni]Source :
- Lecture Notes in Computer Science [ 0302-9743 ] ; 2004.
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.
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DOI: 10.1007/978-3-540-30110-3_157
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