Descent algorithms on oblique manifold for source-adaptive ICA contrast (530 views) (PDF restricted 215 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:
Cardoso, J.-F., Blind signal separation: Statistical principles (1998) Proc IEEE, 86 (10), pp. 2009-2025. , Oc
Plumbley, M.D., Geometrical methods for non-negative ICA: Manifolds, Lie groups and toral subalgebras (2005) Neurocomputing, 67, pp. 161-197. , Aug
Douglas, S.C., Self-stabilized gradient algorithms for blind source separation with orthogonality constraints (2000) IEEE Trans. Neural Netw, 11 (6), pp. 1490-1497. , Nov
Plumbley, M.D., (2004) Lie Group Methods for Optimization with Orthogonality Constraints (Lecture Notes in Computer Science), 3195, pp. 1245-1252. , Berlin, Germany: Springer-Verlag
Fiori, S., Extended Hamiltonian learning on Riemannian manifolds: Numerical aspects (2012) IEEE Trans. Neural Netw. Learn. Syst, 23 (1), pp. 7-21. , Jan
Eriksson, J., Karvanen, J., Koivunen, V., Source distribution adaptive maximum likelihood estimation of ICA model (2000) Proc. 2nd Int. Workshop Independ. Compon. Anal. Blind Signal Separat., pp. 227-232. , Helsinki, Finland Jun
Choi, S., Cichocki, A., Amari, S., Flexible independent component analysis (2000) J. VLSI Signal Process, 26 (1-2), pp. 25-38. , Aug
Karvanen, J., Eriksson, J., Koivunen, V., Pearson system based method for blind separation (2000) Proc. 2nd Int. Workshop Independ. Compon. Anal. Blind Signal Separat., Helsinki, Finland, pp. 585-590. , Jun
Hild, K.E., Erdogmus, D., Príncipe, J., Blind source separation using Renyi's mutual information (2001) IEEE Signal Process. Lett, 8 (6), pp. 174-176. , Jun
Sengupta, K., Burman, P., Sharma, R., A non-parametric approach for independent component analysis using kernel density estimation (2004) Proc IEEE Comput. Soc. Conf. Comput. Vis. Pattern Recognit, 2, pp. 667-672. , Washington DC, Jun-Jul
Boscolo, R., Pan, H., Roychowdhury, V.P., Independent component analysis based on nonparametric density estimation (2004) IEEE Trans. Neural Netw, 15 (1), pp. 55-65. , Jan
Shwartz, S., Zibulevsky, M., Schechner, Y.Y., (2004) ICA Using Kernel Entropy Estimation with NlogN Complexity (Lecture Notes in Computer Science), 3195, pp. 422-429. , Berlin, Germany: Springer-Verlag
Pham, D.-T., Fast algorithms for mutual information based independent component analysis (2004) IEEE Trans. Signal Process, 52 (10), pp. 2690-2700. , Oct
Tsai, D.-M., Lai, S.-C., Independent component analysis-based background subtraction for indoor surveillance (2009) IEEE Trans. Image Process, 18 (1), pp. 158-167. , Jan
Chen, A., (2006) Fast Kernel Density Independent Component Analysis (Lecture Notes in Computer Science), 3889, pp. 24-31. , Berlin, Germany: Springer-Verlag
Xue, Y., Wang, Y., Yang, J., Independent component analysis based on gradient equation and kernel density estimation (2009) Neurocomputing, 72 (7-9), pp. 1597-1604. , Mar
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Chiang, S.-S., Chang, C.-I., Ginsberg, I.W., Unsupervised hyperspectral image analysis using independent component analysis (2000) Proc IEEE Int. Geosci. Remote Sens. Symp, 7, pp. 3136-3138. , Honolulu, HI Jul
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Absil, P.-A., Mahony, R., Sepulchre, R., (2008) Optimization Algorithms on Matrix Manifolds, , Princeton NJ: Princeton Univ. Press
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Selvan, S.E., Amato, U., Qi, C., Gallivan, K.A., Carfora, M.F., Larobina, M., Alfano, B., Unconstrained optimizers for ICA learning on oblique manifold using Parzen density estimation (2011) Dept. Math., Florida State Univ., Tallahassee, Tech. Rep. FSU11-05, , May
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Dai, Y.H., Yuan, Y., An efficient hybrid conjugate gradient method for unconstrained optimization (2001) Ann. Oper. Res, 103 (1-4), pp. 33-47. , Mar
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Selvan, S.E., (2007) Generating Linear Combination of Spectral Images with Mutually Exclusive Specific Information, , Ph.D. dissertation Dept. Inf. Technol. & Math., Univ. de la Méditerranée, Marseille, France Jun
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Bertsekas, D.P., Projected Newton methods for optimization problems with simple constraints (1982) SIAM J. Control Optim, 20 (2), pp. 221-246. , Mar
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Selvan, S.E., Musta̧tea, A., Xavier, C.C., Sequeira, J., Accurate estimation of ICA weight matrix by implicit constraint imposition using Lie group (2009) IEEE Trans. Neural Netw, 20 (10), pp. 1565-1580. , Oct
Li, X.-L., Adalí, T., Independent component analysis by entropy bound minimization (2010) IEEE Trans. Signal Process, 58 (10), pp. 5151-5164. , Oct
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Hyvärinen, A., Fast and robust fixed-point algorithms for independent component analysis (1999) IEEE Trans. Neural Netw, 10 (3), pp. 626-634. , May
Cardoso, J.-F., Souloumiac, A., Blind beamforming for non Gaussian signals (1993) IEE Proc. F, Radar Signal Process, 140 (6), pp. 362-370. , Dec
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Gao, B., Woo, W.L., Dlay, S.S., Variational regularized 2-D nonnegative matrix factorization (2012) IEEE Trans. Neural Netw. Learn. Syst, 23 (5), pp. 703-716. , May
Bach, F.R., Jordan, M.I., Kernel independent component analysis (2002) J. Mach. Learn. Res, 3, pp. 1-48. , Jul
Amato, U., Antoniadis, A., Grégoire, G., Independent component discriminant analysis (2003) Int. Math. J, 3 (7), pp. 735-753
Amari, S., Cichocki, A., Yang, H.H., A new learning algorithm for blind signal separation (1996) Advances in Neural Information Processing Systems, 8, pp. 757-763. , D. S. Touretzky, M. C. Mozer, and M. E. Hasselmo, Eds. Cambridge, MA: MIT Press
Cardoso, J. -F., Blind signal separation: Statistical principles (1998) Proc IEEE, 86 (10), pp. 2009-2025. , Oc
Plumbley, M. D., Geometrical methods for non-negative ICA: Manifolds, Lie groups and toral subalgebras (2005) Neurocomputing, 67, pp. 161-197. , Aug
Douglas, S. C., Self-stabilized gradient algorithms for blind source separation with orthogonality constraints (2000) IEEE Trans. Neural Netw, 11 (6), pp. 1490-1497. , Nov
Plumbley, M. D., (2004) Lie Group Methods for Optimization with Orthogonality Constraints (Lecture Notes in Computer Science), 3195, pp. 1245-1252. , Berlin, Germany: Springer-Verlag
Hild, K. E., Erdogmus, D., Pr ncipe, J., Blind source separation using Renyi's mutual information (2001) IEEE Signal Process. Lett, 8 (6), pp. 174-176. , Jun
Pham, D. -T., Fast algorithms for mutual information based independent component analysis (2004) IEEE Trans. Signal Process, 52 (10), pp. 2690-2700. , Oct
Tsai, D. -M., Lai, S. -C., Independent component analysis-based background subtraction for indoor surveillance (2009) IEEE Trans. Image Process, 18 (1), pp. 158-167. , Jan
Abrudan, T. E., Eriksson, J., Koivunen, V., Steepest descent algorithms for optimization under unitary matrix constraint (2008) IEEE Trans. Signal Process, 56 (3), pp. 1134-1147. , Mar
Lee, T. -W., Wachtler, T., Sejnowski, T. J., Color opponency constitutes a sparse representation for the chromatic structure of natural scenes (2001) Advances in Neural Information Processing Systems, 13, pp. 866-872. , T. K. Leen, T. G. Dietterich, and V. Tresp, Eds. Cambridge, MA: MIT Press
Hyv rinen, A., Karhunen, J., Oja, E., (2001) Independent Component Analysis, , New York: Wiley
Lewicki, M. S., Sejnowski, T. J., Learning overcomplete representations (2000) Neural Comput, 12 (2), pp. 337-365. , Feb
Zhang, W. -T., Lou, S. -T., Iterative algorithm for joint zero diagonalization with application in blind source separation (2011) IEEE Trans. Neural Netw, 22 (7), pp. 1107-1118. , Jul
Douglas, S. C., Amari, S. -I., Kung, S. -Y., On gradient adaptation with unit-norm constraints (2000) IEEE Trans. Signal Process, 48 (6), pp. 1843-1847. , Jun
Absil, P. -A., Gallivan, K. A., Joint diagonalization on the oblique manifold for independent component analysis (2006) Proc. 31st IEEE Int. Conf. Acoust., Speech Signal Process, 5, pp. 945-948. , Toulouse, France May
Shen, H., H per, K., Block Jacobi-type methods for non-orthogonal joint diagonalisation (2009) Proc. 34th IEEE Int. Conf. Acoust., Speech Signal Process., Taipei, Taiwan, pp. 3285-3288. , Apr
Yuen, P. C., Lai, J. H., Face representation using independent component analysis (2002) Pattern Recognit, 35 (6), pp. 1247-1257. , Jun
Chiang, S. -S., Chang, C. -I., Ginsberg, I. W., Unsupervised hyperspectral image analysis using independent component analysis (2000) Proc IEEE Int. Geosci. Remote Sens. Symp, 7, pp. 3136-3138. , Honolulu, HI Jul
Gaucel, J. -M., Guillaume, M., Bourennane, S., (2006) Non Orthogonal Component Analysis: Application to Anomaly Detection (Lecture Notes in Computer Science), 4179, pp. 1198-1209. , Berlin, Germany: Springer-Verlag
Trendafilov, N. T., Lippert, R. A., The multimode Procrustes problem (2002) Linear Algebra Appl, 349, pp. 245-264. , Jul
Depczynski, U., St ckler, J., A differential geometric approach to equidistributed knots on Riemannian manifolds (1998) Approximation Theory IX, Theoretical Aspects, 1, pp. 99-106. , C. K. Chui and L. L. Schumaker, Eds. Nashville, TN: Vanderbilt Univ. Press
Absil, P. -A., Mahony, R., Sepulchre, R., (2008) Optimization Algorithms on Matrix Manifolds, , Princeton NJ: Princeton Univ. Press
Buono, N. D., Elia, C., Computation of few Lyapunov exponents by geodesic based algorithms (2003) Future Generat. Comput. Syst, 19 (3), pp. 425-430. , Apr
Selvan, S. E., Amato, U., Qi, C., Gallivan, K. A., Carfora, M. F., Larobina, M., Alfano, B., Unconstrained optimizers for ICA learning on oblique manifold using Parzen density estimation (2011) Dept. Math., Florida State Univ., Tallahassee, Tech. Rep. FSU11-05, , May
Gilbert, J. C., Nocedal, J., Global convergence properties of conjugate gradient methods for optimization (1992) SIAM J. Optim, 2 (1), pp. 21-42. , Feb
Hager, W. W., Zhang, H., A survey of nonlinear conjugate gradient methods (2006) Pacific J. Optim, 2 (1), pp. 35-58. , Jan
Dai, Y. H., Yuan, Y., An efficient hybrid conjugate gradient method for unconstrained optimization (2001) Ann. Oper. Res, 103 (1-4), pp. 33-47. , Mar
Hestenes, M. R., Stiefel, E., Methods of conjugate gradients for solving linear systems (1952) J. Res. Nat. Bureau Std, 49 (6), pp. 409-436. , Dec
Hager, W. W., A derivative-based bracketing scheme for univariate minimization and the conjugate gradient method (1989) Comput. Math. Appl, 18 (9), pp. 779-795
Powell, M. J. D., Restart procedures for the conjugate gradient method (1977) Math. Program, 12 (1), pp. 241-254. , Dec
Selvan, S. E., (2007) Generating Linear Combination of Spectral Images with Mutually Exclusive Specific Information, , Ph. D. dissertation Dept. Inf. Technol. & Math., Univ. de la M diterran e, Marseille, France Jun
Savas, B., Lim, L. -H., Quasi-Newton methods on Grassmannians and multilinear approximations of tensors (2010) SIAM J. Sci. Comput, 32 (6), pp. 3352-3393. , Nov
Manton, J. H., Optimization algorithms exploiting unitary constraints (2002) IEEE Trans. Signal Process, 50 (3), pp. 635-650. , Mar
Bertsekas, D. P., On the Goldstein-Levitin-Polyak gradient projection method (1976) IEEE Trans. Autom. Control, 21 (2), pp. 174-184. , Apr
Bertsekas, D. P., Projected Newton methods for optimization problems with simple constraints (1982) SIAM J. Control Optim, 20 (2), pp. 221-246. , Mar
Kelley, C. T., (1999) Iterative Methods for Optimization, , Philadelphia PA: SIAM
Rosen, J. B., The gradient projection method for nonlinear programming. Part II. Nonlinear constraints (1961) SIAM J. Appl. Math, 9 (4), pp. 514-532
Luenberger, D. G., The gradient projection method along geodesics (1972) Manage. Sci, 18 (11), pp. 620-631. , Jul
Absil, P. -A., Malick, J., Projection-like retractions on matrix manifolds (2012) SIAM J. Optim, 22 (1), pp. 135-158
Amari, S. -I., Chen, T. -P., Cichocki, A., Nonholonomic orthogonal learning algorithms for blind source separation (2000) Neural Comput, 12 (6), pp. 1463-1484. , Jul
Selvan, S. E., Musta tea, A., Xavier, C. C., Sequeira, J., Accurate estimation of ICA weight matrix by implicit constraint imposition using Lie group (2009) IEEE Trans. Neural Netw, 20 (10), pp. 1565-1580. , Oct
Li, X. -L., Adal, T., Independent component analysis by entropy bound minimization (2010) IEEE Trans. Signal Process, 58 (10), pp. 5151-5164. , Oct
Jankovic, M. V., Sugiyama, M., A multipurpose linear component analysis method based on modulated Hebb-Oja learning rule (2008) IEEE Signal Process. Lett, 15, pp. 677-680
Hyv rinen, A., Fast and robust fixed-point algorithms for independent component analysis (1999) IEEE Trans. Neural Netw, 10 (3), pp. 626-634. , May
Cardoso, J. -F., Souloumiac, A., Blind beamforming for non Gaussian signals (1993) IEE Proc. F, Radar Signal Process, 140 (6), pp. 362-370. , Dec
Gao, B., Woo, W. L., Dlay, S. S., Variational regularized 2-D nonnegative matrix factorization (2012) IEEE Trans. Neural Netw. Learn. Syst, 23 (5), pp. 703-716. , May
Bach, F. R., Jordan, M. I., Kernel independent component analysis (2002) J. Mach. Learn. Res, 3, pp. 1-48. , Jul
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:
Cardoso, J.-F., Blind signal separation: Statistical principles (1998) Proc IEEE, 86 (10), pp. 2009-2025. , Oc
Plumbley, M.D., Geometrical methods for non-negative ICA: Manifolds, Lie groups and toral subalgebras (2005) Neurocomputing, 67, pp. 161-197. , Aug
Douglas, S.C., Self-stabilized gradient algorithms for blind source separation with orthogonality constraints (2000) IEEE Trans. Neural Netw, 11 (6), pp. 1490-1497. , Nov
Plumbley, M.D., (2004) Lie Group Methods for Optimization with Orthogonality Constraints (Lecture Notes in Computer Science), 3195, pp. 1245-1252. , Berlin, Germany: Springer-Verlag
Fiori, S., Extended Hamiltonian learning on Riemannian manifolds: Numerical aspects (2012) IEEE Trans. Neural Netw. Learn. Syst, 23 (1), pp. 7-21. , Jan
Eriksson, J., Karvanen, J., Koivunen, V., Source distribution adaptive maximum likelihood estimation of ICA model (2000) Proc. 2nd Int. Workshop Independ. Compon. Anal. Blind Signal Separat., pp. 227-232. , Helsinki, Finland Jun
Choi, S., Cichocki, A., Amari, S., Flexible independent component analysis (2000) J. VLSI Signal Process, 26 (1-2), pp. 25-38. , Aug
Karvanen, J., Eriksson, J., Koivunen, V., Pearson system based method for blind separation (2000) Proc. 2nd Int. Workshop Independ. Compon. Anal. Blind Signal Separat., Helsinki, Finland, pp. 585-590. , Jun
Hild, K.E., Erdogmus, D., Príncipe, J., Blind source separation using Renyi's mutual information (2001) IEEE Signal Process. Lett, 8 (6), pp. 174-176. , Jun
Sengupta, K., Burman, P., Sharma, R., A non-parametric approach for independent component analysis using kernel density estimation (2004) Proc IEEE Comput. Soc. Conf. Comput. Vis. Pattern Recognit, 2, pp. 667-672. , Washington DC, Jun-Jul
Boscolo, R., Pan, H., Roychowdhury, V.P., Independent component analysis based on nonparametric density estimation (2004) IEEE Trans. Neural Netw, 15 (1), pp. 55-65. , Jan
Shwartz, S., Zibulevsky, M., Schechner, Y.Y., (2004) ICA Using Kernel Entropy Estimation with NlogN Complexity (Lecture Notes in Computer Science), 3195, pp. 422-429. , Berlin, Germany: Springer-Verlag
Pham, D.-T., Fast algorithms for mutual information based independent component analysis (2004) IEEE Trans. Signal Process, 52 (10), pp. 2690-2700. , Oct
Tsai, D.-M., Lai, S.-C., Independent component analysis-based background subtraction for indoor surveillance (2009) IEEE Trans. Image Process, 18 (1), pp. 158-167. , Jan
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Shen, H., H per, K., Block Jacobi-type methods for non-orthogonal joint diagonalisation (2009) Proc. 34th IEEE Int. Conf. Acoust., Speech Signal Process., Taipei, Taiwan, pp. 3285-3288. , Apr
Yuen, P. C., Lai, J. H., Face representation using independent component analysis (2002) Pattern Recognit, 35 (6), pp. 1247-1257. , Jun
Chiang, S. -S., Chang, C. -I., Ginsberg, I. W., Unsupervised hyperspectral image analysis using independent component analysis (2000) Proc IEEE Int. Geosci. Remote Sens. Symp, 7, pp. 3136-3138. , Honolulu, HI Jul
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Selvan, S. E., Amato, U., Qi, C., Gallivan, K. A., Carfora, M. F., Larobina, M., Alfano, B., Unconstrained optimizers for ICA learning on oblique manifold using Parzen density estimation (2011) Dept. Math., Florida State Univ., Tallahassee, Tech. Rep. FSU11-05, , May
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Hager, W. W., Zhang, H., A survey of nonlinear conjugate gradient methods (2006) Pacific J. Optim, 2 (1), pp. 35-58. , Jan
Dai, Y. H., Yuan, Y., An efficient hybrid conjugate gradient method for unconstrained optimization (2001) Ann. Oper. Res, 103 (1-4), pp. 33-47. , Mar
Hestenes, M. R., Stiefel, E., Methods of conjugate gradients for solving linear systems (1952) J. Res. Nat. Bureau Std, 49 (6), pp. 409-436. , Dec
Hager, W. W., A derivative-based bracketing scheme for univariate minimization and the conjugate gradient method (1989) Comput. Math. Appl, 18 (9), pp. 779-795
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Selvan, S. E., (2007) Generating Linear Combination of Spectral Images with Mutually Exclusive Specific Information, , Ph. D. dissertation Dept. Inf. Technol. & Math., Univ. de la M diterran e, Marseille, France Jun
Savas, B., Lim, L. -H., Quasi-Newton methods on Grassmannians and multilinear approximations of tensors (2010) SIAM J. Sci. Comput, 32 (6), pp. 3352-3393. , Nov
Manton, J. H., Optimization algorithms exploiting unitary constraints (2002) IEEE Trans. Signal Process, 50 (3), pp. 635-650. , Mar
Bertsekas, D. P., On the Goldstein-Levitin-Polyak gradient projection method (1976) IEEE Trans. Autom. Control, 21 (2), pp. 174-184. , Apr
Bertsekas, D. P., Projected Newton methods for optimization problems with simple constraints (1982) SIAM J. Control Optim, 20 (2), pp. 221-246. , Mar
Kelley, C. T., (1999) Iterative Methods for Optimization, , Philadelphia PA: SIAM
Rosen, J. B., The gradient projection method for nonlinear programming. Part II. Nonlinear constraints (1961) SIAM J. Appl. Math, 9 (4), pp. 514-532
Luenberger, D. G., The gradient projection method along geodesics (1972) Manage. Sci, 18 (11), pp. 620-631. , Jul
Absil, P. -A., Malick, J., Projection-like retractions on matrix manifolds (2012) SIAM J. Optim, 22 (1), pp. 135-158
Amari, S. -I., Chen, T. -P., Cichocki, A., Nonholonomic orthogonal learning algorithms for blind source separation (2000) Neural Comput, 12 (6), pp. 1463-1484. , Jul
Selvan, S. E., Musta tea, A., Xavier, C. C., Sequeira, J., Accurate estimation of ICA weight matrix by implicit constraint imposition using Lie group (2009) IEEE Trans. Neural Netw, 20 (10), pp. 1565-1580. , Oct
Li, X. -L., Adal, T., Independent component analysis by entropy bound minimization (2010) IEEE Trans. Signal Process, 58 (10), pp. 5151-5164. , Oct
Jankovic, M. V., Sugiyama, M., A multipurpose linear component analysis method based on modulated Hebb-Oja learning rule (2008) IEEE Signal Process. Lett, 15, pp. 677-680
Hyv rinen, A., Fast and robust fixed-point algorithms for independent component analysis (1999) IEEE Trans. Neural Netw, 10 (3), pp. 626-634. , May
Cardoso, J. -F., Souloumiac, A., Blind beamforming for non Gaussian signals (1993) IEE Proc. F, Radar Signal Process, 140 (6), pp. 362-370. , Dec
Gao, B., Woo, W. L., Dlay, S. S., Variational regularized 2-D nonnegative matrix factorization (2012) IEEE Trans. Neural Netw. Learn. Syst, 23 (5), pp. 703-716. , May
Bach, F. R., Jordan, M. I., Kernel independent component analysis (2002) J. Mach. Learn. Res, 3, pp. 1-48. , Jul
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 (313 views) (PDF 274 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 (313 views) (PDF 274 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
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Total impact factor: 0.086 (0 excluding Abstracts).
Total 5 year impact factor: 0.315 (0 excluding Abstracts).
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