Descent algorithms on oblique manifold for source-adaptive ICA contrast (779 views) (PDF restricted 271 views)
Ieee Trans Neural Networks Learn Sys (ISSN: 2162-237x, 2162-2388), 2012 Dec; 23(12): 1930-1947.
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Paper type: Journal Article,
Impact factor: 3.766, 5-year impact factor: 3.632
Url: http://www.scopus.com/inward/record.url?eid=2-s2.0-84876904976&partnerID=40&md5=eacba3831a59a7dc2dc5a0e16afafe29
Keywords: Conjugate Gradient, Oblique Manifold, Parzen Window, Quasi-Newton, Retraction, Steepest Descent, Vector Transport, Algorithms, Conjugate Gradient Method, Newton-Raphson Method, Optimization, Quality Control, Independent Component Analysis,
Affiliations:
*** IBB - CNR ***
Department of Mathematical Engineering, Université Catholique de Louvain, Louvain-la-Neuve 1348, Belgium
Istituto per le Applicazioni Del Calcolo Mauro Picone-Sede di Napoli, Consiglio Nazionale Delle Ricerche, Naples 80131, Italy
Istituto di Biostrutture e Bioimmagini, Consiglio Nazionale Delle Ricerche, Naples 80131, Italy
References:
Not available.
Ieee Trans Neural Networks Learn Sys (ISSN: 2162-237x, 2162-2388), 2012 Dec; 23(12): 1930-1947.
Export to BibTeX Export to EndNote
Paper type: Journal Article,
Impact factor: 3.766, 5-year impact factor: 3.632
Url: http://www.scopus.com/inward/record.url?eid=2-s2.0-84876904976&partnerID=40&md5=eacba3831a59a7dc2dc5a0e16afafe29
Keywords: Conjugate Gradient, Oblique Manifold, Parzen Window, Quasi-Newton, Retraction, Steepest Descent, Vector Transport, Algorithms, Conjugate Gradient Method, Newton-Raphson Method, Optimization, Quality Control, Independent Component Analysis,
Affiliations:
*** IBB - CNR ***
Department of Mathematical Engineering, Université Catholique de Louvain, Louvain-la-Neuve 1348, Belgium
Istituto per le Applicazioni Del Calcolo Mauro Picone-Sede di Napoli, Consiglio Nazionale Delle Ricerche, Naples 80131, Italy
Istituto di Biostrutture e Bioimmagini, Consiglio Nazionale Delle Ricerche, Naples 80131, Italy
References:
Not available.
Descent algorithms on oblique manifold for source-adaptive ICA contrast
A Riemannian manifold optimization strategy is proposed to facilitate the relaxation of the orthonormality constraint in a more natural way in the course of performing independent component analysis (ICA) that employs a mutual information-based source-adaptive contrast function. Despite the extensive development of manifold techniques catering to the orthonormality constraint, only a limited number of works have been dedicated to oblique manifold (OB) algorithms to intrinsically handle the normality constraint, which has been empirically shown to be superior to other Riemannian and Euclidean approaches. Imposing the normality constraint implicitly, in line with the ICA definition, essentially guarantees a substantial improvement in the solution accuracy, by way of increased degrees of freedom while searching for an optimal unmixing ICA matrix, in contrast with the orthonormality constraint. Designs of the steepest descent, conjugate gradient with Hager-Zhang or a hybrid update parameter, quasi-Newton, and cost-effective quasi-Newton methods intended for OB are presented in this paper. Their performance is validated using natural images and systematically compared with the popular state-of-the-art approaches in order to assess the performance effects of the choice of algorithm and the use of a Riemannian rather than Euclidean framework. We surmount the computational challenge associated with the direct estimation of the source densities using the improved fast Gauss transform in the evaluation of the contrast function and its gradient. The proposed OB schemes may find applications in the offline image/signal analysis, wherein, on one hand, the computational overhead can be tolerated, and, on the other, the solution quality holds paramount interest. © 2012 IEEE.
A Riemannian manifold optimization strategy is proposed to facilitate the relaxation of the orthonormality constraint in a more natural way in the course of performing independent component analysis (ICA) that employs a mutual information-based source-adaptive contrast function. Despite the extensive development of manifold techniques catering to the orthonormality constraint, only a limited number of works have been dedicated to oblique manifold (OB) algorithms to intrinsically handle the normality constraint, which has been empirically shown to be superior to other Riemannian and Euclidean approaches. Imposing the normality constraint implicitly, in line with the ICA definition, essentially guarantees a substantial improvement in the solution accuracy, by way of increased degrees of freedom while searching for an optimal unmixing ICA matrix, in contrast with the orthonormality constraint. Designs of the steepest descent, conjugate gradient with Hager-Zhang or a hybrid update parameter, quasi-Newton, and cost-effective quasi-Newton methods intended for OB are presented in this paper. Their performance is validated using natural images and systematically compared with the popular state-of-the-art approaches in order to assess the performance effects of the choice of algorithm and the use of a Riemannian rather than Euclidean framework. We surmount the computational challenge associated with the direct estimation of the source densities using the improved fast Gauss transform in the evaluation of the contrast function and its gradient. The proposed OB schemes may find applications in the offline image/signal analysis, wherein, on one hand, the computational overhead can be tolerated, and, on the other, the solution quality holds paramount interest. © 2012 IEEE.
Descent algorithms on oblique manifold for source-adaptive ICA contrast
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Descent algorithms on oblique manifold for source-adaptive ICA contrast
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Selvan SE, Amato U, Qic C, Gallivanc KA, Carfora MF, Larobina M, Alfano B
* Unconstrained Optimizers For Ica Learning On Oblique Manifold Using Parzen Density Estimation (626 views) (PDF 317 views)
Dept Math Florida State Univ Tallahassee Tech Rep Fsu11 05, 2011; N/D: N/D-N/D.
Impact Factor: 0.086
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* Unconstrained Optimizers For Ica Learning On Oblique Manifold Using Parzen Density Estimation (626 views) (PDF 317 views)
Dept Math Florida State Univ Tallahassee Tech Rep Fsu11 05, 2011; N/D: N/D-N/D.
Impact Factor: 0.086
View Export to BibTeX Export to EndNote
1 Records (0 excluding Abstracts).
Total impact factor: 0.086 (0 excluding Abstracts).
Total 5 year impact factor: 0.315 (0 excluding Abstracts).
Total impact factor: 0.086 (0 excluding Abstracts).
Total 5 year impact factor: 0.315 (0 excluding Abstracts).
779 views. Last view on Friday 18 April 2025, 17:16:49
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