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Non-negative Independent Component Analysis Algorithm Based on 2D Givens Rotations and a Newton Optimization

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Latent Variable Analysis and Signal Separation (LVA/ICA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6365))

Abstract

In this paper, we consider the Independent Component Analysis problem when the hidden sources are non-negative (Non-negative ICA). This problem is formulated as a non-linear cost function optimization over the special orthogonal matrix group SO(n). Using Givens rotations and Newton optimization, we developed an effective axis pair rotation method for Non-negative ICA. The performance of the proposed method is compared to those designed by Plumbley and simulations on synthetic data show the efficiency of the proposed algorithm.

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References

  1. Plumbley, M.: Conditions for Nonnegative Independent Component Analysis. IEEE Signal Processing Letters 9, 177–180 (2002)

    Article  Google Scholar 

  2. Plumbley, M.: Algorithms for Nonnegative Independent Component Analysis. IEEE Transactions on Neural Networks 14, 534–543 (2003)

    Article  Google Scholar 

  3. Comon, P.: Independent component analysis. A new concept? Signal Processing 36, 287–314 (1994)

    Article  MATH  Google Scholar 

  4. Cardoso, J.F., Souloumiac, A.: Blind Beamforming for Non Gaussian Signal. IEE Proceedings-F 140, 362–370 (1993)

    Google Scholar 

  5. Hyvärinen, A.: Fast and Robust Fixed-Point Algorithms for Independent Component Analysis. IEEE Transactions on Neural Networks 10, 626–634 (1999)

    Article  Google Scholar 

  6. Lee, D.D., Seung, H.S.: Algorithms for Non-negative Matrix Factorization. In: 14th Annual Neural Information Processing Systems Conference. NIPS, Denver (2000)

    Google Scholar 

  7. Lin, C.J.: Projected Gradient Methods for Non-negative Matrix Factorization. Neural Computation 19, 2756–2779 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  8. Laurberg, H.: Uniqueness of Non-negative Matrix Factorization. In: IEEE Statistical Signal Processing Workshop, pp. 49–53 (2007)

    Google Scholar 

  9. Theis, F.J., Stadlthanner, K., Tanaka, T.: First Results on Uniqueness of Sparse Non-negative Matrix Factorization. In: EUSIPCO 2005 (2005)

    Google Scholar 

  10. Donoho, D., Stodden, V.: When Does Non-Negative Matrix Factorization Give a Correct Decomposition into Parts? Advances in Neural Information Processing Systems 16, 1141–1148 (2003)

    Google Scholar 

  11. Plumbley, M., Oja, E.: A “Nonnegative PCA” Algorithm for Independent Component Analysis. IEEE Transactions on Neural Networks 15, 66–76 (2004)

    Article  Google Scholar 

  12. Li, Y., Zheng, H.: Improvement for Nonnegative PCA Algorithm for Independent Component Analysis. In: Neural Networks and Brain, ICNN&B, International Conference on, 2000–2002 (2005)

    Google Scholar 

  13. Cichocki, A., Zdunek, R., Phan, A.H., Amari, S.: Nonnegative Matrix and Tensor Factorizations Applications to Exploratory Multi-way Data Analysis and Blind Source Separation. John Wiley & Sons, Ltd., Chichester (2009)

    Google Scholar 

  14. Paatero, P.: Least Squares Formulation of robust non-negative factor analysis. Chemometrics and Intelligent Laboratory Systems 37, 23–35 (1997)

    Article  Google Scholar 

  15. Plumbley, M.: Optimization using Fourier Expansion over a Geodesic for Non-Negative ICA. In: Puntonet, C.G., Prieto, A.G. (eds.) ICA 2004. LNCS, vol. 3195, pp. 44–56. Springer, Heidelberg (2004)

    Google Scholar 

  16. Plumbley, M.: Geometrical methods for non-negative ICA: Manifolds, Lie groups and toral subalgebras. Neurocomputing 67, 161–197 (2005)

    Article  Google Scholar 

  17. Bronstein, A.M., Bronstein, M.M., Zibulevsky, M., Zeevi, Y.Y.: Sparse ICA for Blind Separation of Transmitted and Reflected Images. Wiley Periodicals, 84–91 (2005)

    Google Scholar 

  18. Hoyer, P.O.: Non-negative Matrix Factorization with Sparseness Constraints. Journal of Machine Learning Research 5, 1457–1469 (2004)

    MathSciNet  Google Scholar 

  19. Moussaoui, S., Brie, D., Mohammad-Djafari, A., Carteret, C.: Separation of Non-Negative Mixture of Non-Negative Sources Using a Bayesian Approach and MCMC Sampling. IEEE Transactions on Signal Processing 54, 4133–4145 (2006)

    Article  Google Scholar 

  20. Duarte, L.T., Jutten, C., Moussaoui, S.: A Bayesian Nonlinear Source Separation Method for Smart Ion-Selective Electrode Arrays. IEEE Sensors Journal 9, 1763–1771 (2009)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. CEA, LIST, Laboratoire d’Outils pour l’Analyse de Données, Gif-sur-Yvette, F-91191, France

    Wendyam Serge Boris Ouedraogo & Antoine Souloumiac

  2. Unité Signaux et Systèmes, National School of Engineers of Tunis, BP 37, 1002, Tunis, Tunisia

    Wendyam Serge Boris Ouedraogo

  3. GIPSA-lab, UMR 5216 CNRS, University of Grenoble, 961 rue de la Houille Blanche, BP 46, F-38402, Grenoble Cedex, France

    Wendyam Serge Boris Ouedraogo & Christian Jutten

Authors
  1. Wendyam Serge Boris Ouedraogo
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  2. Antoine Souloumiac
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  3. Christian Jutten
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Editor information

Editors and Affiliations

  1. Dept. of Electrical Engineering, Universitè d’Evry Val d’Essone, 40 rue du Pelvoux, 91020, Courcouronnes, France

    Vincent Vigneron

  2. Laboratoire I3S, Les Algorithmes - Euclide-B, BP 121, Université de Nice-Sophia Antipolis, 2000 Route des Lucioles, 06903, Sophia Antipolis Cedex, France

    Vicente Zarzoso

  3. School of Engineering, Dept. of Telecommunications, ISITSchool of Engineering, Dept. of Telecommunications, ISITV, Université de Toulon, Avenue George Pompidou, BP 56, La Valette du Var, Cedex, 83162, France

    Eric Moreau

  4. INRIA France, Equipe-projet METISS, Centre de Recherche INRIA Rennes-Bretagne Atlantique, Campus de Beaulieu, 35042, Rennes cedex, France

    Rémi Gribonval

  5. INRIA France, Equipe-projet METISS, Centre de Recherche INRIA Rennes-Bretagne Atlantique, Campus de Beaulieu, 35042, Rennes Cedex, France

    Emmanuel Vincent

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Ouedraogo, W.S.B., Souloumiac, A., Jutten, C. (2010). Non-negative Independent Component Analysis Algorithm Based on 2D Givens Rotations and a Newton Optimization. In: Vigneron, V., Zarzoso, V., Moreau, E., Gribonval, R., Vincent, E. (eds) Latent Variable Analysis and Signal Separation. LVA/ICA 2010. Lecture Notes in Computer Science, vol 6365. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15995-4_65

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  • DOI: https://doi.org/10.1007/978-3-642-15995-4_65

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15994-7

  • Online ISBN: 978-3-642-15995-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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