Lie Group Methods for Optimization with Orthogonality Constraints
Identifieur interne : 000834 ( Main/Exploration ); précédent : 000833; suivant : 000835Lie 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.
Url:
DOI: 10.1007/978-3-540-30110-3_157
Affiliations:
Links toward previous steps (curation, corpus...)
Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">Lie Group Methods for Optimization with Orthogonality Constraints</title>
<author><name sortKey="Plumbley, D" sort="Plumbley, D" uniqKey="Plumbley D" first="D." last="Plumbley">D. Plumbley</name>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">ISTEX</idno>
<idno type="RBID">ISTEX:FE2C407982B78EAB754C83671C0DF725862957C5</idno>
<date when="2004" year="2004">2004</date>
<idno type="doi">10.1007/978-3-540-30110-3_157</idno>
<idno type="url">https://api.istex.fr/document/FE2C407982B78EAB754C83671C0DF725862957C5/fulltext/pdf</idno>
<idno type="wicri:Area/Main/Corpus">001072</idno>
<idno type="wicri:Area/Main/Curation">001030</idno>
<idno type="wicri:Area/Main/Exploration">000834</idno>
<idno type="wicri:explorRef" wicri:stream="Main" wicri:step="Exploration">000834</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Lie Group Methods for Optimization with Orthogonality Constraints</title>
<author><name sortKey="Plumbley, D" sort="Plumbley, D" uniqKey="Plumbley D" first="D." last="Plumbley">D. Plumbley</name>
<affiliation wicri:level="4"><country xml:lang="fr">Royaume-Uni</country>
<wicri:regionArea>Department of Electronic Engineering, Queen Mary University of London, Mile End Road, E1 4NS, London</wicri:regionArea>
<placeName><settlement type="city">Londres</settlement>
<region type="country">Angleterre</region>
<region type="région" nuts="1">Grand Londres</region>
</placeName>
<orgName type="university">Université de Londres</orgName>
</affiliation>
<affiliation wicri:level="1"><country wicri:rule="url">Royaume-Uni</country>
</affiliation>
</author>
</analytic>
<monogr></monogr>
<series><title level="s">Lecture Notes in Computer Science</title>
<imprint><date>2004</date>
</imprint>
<idno type="ISSN">0302-9743</idno>
<idno type="eISSN">1611-3349</idno>
<idno type="ISSN">0302-9743</idno>
</series>
<idno type="istex">FE2C407982B78EAB754C83671C0DF725862957C5</idno>
<idno type="DOI">10.1007/978-3-540-30110-3_157</idno>
<idno type="ChapterID">Chap157</idno>
<idno type="ChapterID">157</idno>
</biblStruct>
</sourceDesc>
<seriesStmt><idno type="ISSN">0302-9743</idno>
</seriesStmt>
</fileDesc>
<profileDesc><textClass></textClass>
<langUsage><language ident="en">en</language>
</langUsage>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml:lang="en">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.</div>
</front>
</TEI>
<affiliations><list><country><li>Royaume-Uni</li>
</country>
<region><li>Angleterre</li>
<li>Grand Londres</li>
</region>
<settlement><li>Londres</li>
</settlement>
<orgName><li>Université de Londres</li>
</orgName>
</list>
<tree><country name="Royaume-Uni"><region name="Angleterre"><name sortKey="Plumbley, D" sort="Plumbley, D" uniqKey="Plumbley D" first="D." last="Plumbley">D. Plumbley</name>
</region>
<name sortKey="Plumbley, D" sort="Plumbley, D" uniqKey="Plumbley D" first="D." last="Plumbley">D. Plumbley</name>
</country>
</tree>
</affiliations>
</record>
Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Musique/explor/SchutzV1/Data/Main/Exploration
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000834 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 000834 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien |wiki= Wicri/Musique |area= SchutzV1 |flux= Main |étape= Exploration |type= RBID |clé= ISTEX:FE2C407982B78EAB754C83671C0DF725862957C5 |texte= Lie Group Methods for Optimization with Orthogonality Constraints }}
This area was generated with Dilib version V0.6.38. |