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Dimensionality Reduction in ICA and Rank-(R 1,R 2,...,R N) Reduction in Multilinear Algebra

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Independent Component Analysis and Blind Signal Separation (ICA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3195))

Abstract

We show that the best rank-(R 1,R 2,...,R N) approximation in multilinear algebra is a powerful tool for dimensionality reduction in ICA schemes without prewhitening. We consider the application to different classes of ICA algorithms.

L. De Lathauwer holds a permanent research position with the French C.N.R.S.; he also holds a honorary position with the K.U.Leuven. J. Vandewalle is a Full Professor with the K.U.Leuven. Part of this research was supported by the Research Council K.U.Leuven (GOA-MEFISTO-666), the Flemish Government (F.W.O. project G.0240.99, F.W.O. Research Communities ICCoS and ANMMM, Tournesol project T2004.13) and the Belgian Federal Government (IUAP V-22).

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References

  1. André, T.F., Nowak, R.D., Van Veen, B.D.: Low-rank estimation of higher order statistics. IEEE Trans. Signal Processing. 45, 673–685 (1997)

    Article  Google Scholar 

  2. Belouchrani, A., Abed-Meraim, K., Cardoso, J.-F., Moulines, E.: A blind source separation technique using second order statistics. IEEE Trans. Signal Processing 45, 434–444 (1997)

    Article  Google Scholar 

  3. Bro, R.: PARAFAC. Tutorial & applications. Chemom. Intell. Lab. Syst. 38, 149–171 (1997)

    Article  Google Scholar 

  4. Cardoso, J.-F.: On the performance of orthogonal source separation algorithms. In: Proc. EUSIPCO 1994, Edinburgh, Scotland, U.K. pp. 776–779 (1994)

    Google Scholar 

  5. Cardoso, J.-F., Souloumiac, A.: Blind beamforming for non-Gaussian signals. IEE Proc.-F 140, 362–370 (1994)

    Google Scholar 

  6. Cruces, S., Cichocki, A., De Lathauwer, L.: Thin QR and SVD factorizations for simultaneous blind signal extraction. In: Proc. EUSIPCO 2004, Vienna, Austria (2004)

    Google Scholar 

  7. De Lathauwer, L., De Moor, B., Vandewalle, J.: A multilinear singular value decomposition. SIAM J. Matrix Anal. Appl. 21, 1253–1278 (2000)

    Article  MathSciNet  Google Scholar 

  8. De Lathauwer, L., De Moor, B., Vandewalle, J.: On the best rank-1 and rank- (R1,R2,., RN) approximation of higher-order tensors. SIAM J. Matrix Anal. Appl. 21, 1324–1342 (2000)

    Article  MathSciNet  Google Scholar 

  9. De Lathauwer, L., Vandewalle, J.: Dimensionality reduction in higher-order signal processing and rank-(R1,R2,.,RN) reduction in multilinear algebra. Lin. Alg. Appl. (to appear)

    Google Scholar 

  10. De Lathauwer, L., De Moor, B., Vandewalle, J.: Computation of the canonical decomposition by means of a simultaneous generalized Schur decompositition. SIAM J. Matrix Anal. Appl. (to appear)

    Google Scholar 

  11. De Lathauwer, L., De Moor, B., Vandewalle, J.: A prewhitening-induced bound on the identification error in independent component analysis, Tech. report

    Google Scholar 

  12. De Lathauwer, L., Hoegaerts, L., Vandewalle, J.: A Grassmann-Rayleigh quotient iteration for dimensionality reduction in ICA. In: Puntonet, C.G., Prieto, A.G. (eds.) ICA 2004. LNCS, vol. 3195, pp. 335–342. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  13. Golub, G.H., Van Loan, C.F.: Matrix Computations. Johns Hopkins University Press, Baltimore (1996)

    MATH  Google Scholar 

  14. Kroonenberg, P.M.: Three-mode principal component analysis. DSWO Press, Leiden (1983)

    MATH  Google Scholar 

  15. Leurgans, S.E., Ross, R.T., Abel, R.B.: A decomposition for three-way arrays. SIAM J. Matrix Anal. Appl. 14, 1064–1083 (1993)

    Article  MathSciNet  Google Scholar 

  16. Pham, D.-T., Cardoso, J.-F.: Blind separation of instantaneous mixtures of nonstationary sources. IEEE Trans. Signal Processing. 49, 1837–1848 (2001)

    Article  MathSciNet  Google Scholar 

  17. Pham, D.-T.: Joint approximate diagonalization of positive definite Hermitian matrices. SIAM J. Matrix Anal. Appl. 22, 1136–1152 (2001)

    Article  MathSciNet  Google Scholar 

  18. Tucker, L.R.: Some mathematical notes on three-mode factor analysis. Psychometrika 31, 279–311 (1966)

    Article  MathSciNet  Google Scholar 

  19. Yeredor, A.: Non-orthogonal joint diagonalization in the least-squares sense with application in blind source separation. IEEE Trans. Signal Processing 50, 1545–1553 (2002)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. ETIS (CNRS, ENSEA, UCP), UMR 8051, Cergy-Pontoise, France

    Lieven De Lathauwer

  2. E.E. Dept. (ESAT) – SCD, K.U.Leuven, Leuven, Belgium

    Lieven De Lathauwer & Joos Vandewalle

Authors
  1. Lieven De Lathauwer
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  2. Joos Vandewalle
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Editor information

Editors and Affiliations

  1. Dept. of Architecture and Computer Technology, University of Granada, Spain

    Carlos G. Puntonet  & Alberto Prieto  & 

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De Lathauwer, L., Vandewalle, J. (2004). Dimensionality Reduction in ICA and Rank-(R 1,R 2,...,R N) Reduction in Multilinear Algebra. In: Puntonet, C.G., Prieto, A. (eds) Independent Component Analysis and Blind Signal Separation. ICA 2004. Lecture Notes in Computer Science, vol 3195. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30110-3_38

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  • DOI: https://doi.org/10.1007/978-3-540-30110-3_38

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23056-4

  • Online ISBN: 978-3-540-30110-3

  • eBook Packages: Springer Book Archive

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