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Lie Group Methods for Optimization with Orthogonality Constraints

  • Mark D. Plumbley
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3195)

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.

Keywords

Line Search Steep Descent Conjugate Gradient Method Independent Component Analysis Conjugate Gradient Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Mark D. Plumbley
    • 1
  1. 1.Department of Electronic EngineeringQueen Mary University of LondonLondonUK

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