File Download
There are no files associated with this item.
Links for fulltext
(May Require Subscription)
- Publisher Website: 10.1007/s10957-011-9832-4
- Scopus: eid_2-s2.0-84876877752
- WOS: WOS:000318283900015
- Find via
Supplementary
- Citations:
- Appears in Collections:
Article: Superlinear Convergence of a General Algorithm for the Generalized Foley-Sammon Discriminant Analysis
Title | Superlinear Convergence of a General Algorithm for the Generalized Foley-Sammon Discriminant Analysis |
---|---|
Authors | |
Keywords | Superlinear convergence Linear discriminant analysis Generalized Foley-Sammon transform Dimensionality reduction The trace ratio optimization problem |
Issue Date | 2013 |
Citation | Journal of Optimization Theory and Applications, 2013, v. 157, n. 3, p. 853-865 How to Cite? |
Abstract | Linear Discriminant Analysis (LDA) is one of the most efficient statistical approaches for feature extraction and dimension reduction. The generalized Foley-Sammon transform and the trace ratio model are very important in LDA and have received increasing interest. An efficient iterative method has been proposed for the resulting trace ratio optimization problem, which, under a mild assumption, is proved to enjoy both the local quadratic convergence and the global convergence to the global optimal solution (Zhang, L.-H., Liao, L.-Z., Ng, M. K.: SIAM J. Matrix Anal. Appl. 31:1584, 2010). The present paper further investigates the convergence behavior of this iterative method under no assumption. In particular, we prove that the iteration converges superlinearly when the mild assumption is removed. All possible limit points are characterized as a special subset of the global optimal solutions. An illustrative numerical example is also presented. © 2011 Springer Science+Business Media, LLC. |
Persistent Identifier | http://hdl.handle.net/10722/276949 |
ISSN | 2023 Impact Factor: 1.6 2023 SCImago Journal Rankings: 0.864 |
ISI Accession Number ID |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Zhang, Lei Hong | - |
dc.contributor.author | Liao, Li Zhi | - |
dc.contributor.author | Ng, Michael K. | - |
dc.date.accessioned | 2019-09-18T08:35:08Z | - |
dc.date.available | 2019-09-18T08:35:08Z | - |
dc.date.issued | 2013 | - |
dc.identifier.citation | Journal of Optimization Theory and Applications, 2013, v. 157, n. 3, p. 853-865 | - |
dc.identifier.issn | 0022-3239 | - |
dc.identifier.uri | http://hdl.handle.net/10722/276949 | - |
dc.description.abstract | Linear Discriminant Analysis (LDA) is one of the most efficient statistical approaches for feature extraction and dimension reduction. The generalized Foley-Sammon transform and the trace ratio model are very important in LDA and have received increasing interest. An efficient iterative method has been proposed for the resulting trace ratio optimization problem, which, under a mild assumption, is proved to enjoy both the local quadratic convergence and the global convergence to the global optimal solution (Zhang, L.-H., Liao, L.-Z., Ng, M. K.: SIAM J. Matrix Anal. Appl. 31:1584, 2010). The present paper further investigates the convergence behavior of this iterative method under no assumption. In particular, we prove that the iteration converges superlinearly when the mild assumption is removed. All possible limit points are characterized as a special subset of the global optimal solutions. An illustrative numerical example is also presented. © 2011 Springer Science+Business Media, LLC. | - |
dc.language | eng | - |
dc.relation.ispartof | Journal of Optimization Theory and Applications | - |
dc.subject | Superlinear convergence | - |
dc.subject | Linear discriminant analysis | - |
dc.subject | Generalized Foley-Sammon transform | - |
dc.subject | Dimensionality reduction | - |
dc.subject | The trace ratio optimization problem | - |
dc.title | Superlinear Convergence of a General Algorithm for the Generalized Foley-Sammon Discriminant Analysis | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1007/s10957-011-9832-4 | - |
dc.identifier.scopus | eid_2-s2.0-84876877752 | - |
dc.identifier.volume | 157 | - |
dc.identifier.issue | 3 | - |
dc.identifier.spage | 853 | - |
dc.identifier.epage | 865 | - |
dc.identifier.eissn | 1573-2878 | - |
dc.identifier.isi | WOS:000318283900015 | - |
dc.identifier.issnl | 0022-3239 | - |