Second Order Subspace Analysis and Simple Decompositions

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6365)


The recovery of the mixture of an N-dimensional signal generated by N independent processes is a well studied problem (see e.g. [1,10]) and robust algorithms that solve this problem by Joint Diagonalization exist. While there is a lot of empirical evidence suggesting that these algorithms are also capable of solving the case where the source signals have block structure (apart from a final permutation recovery step), this claim could not be shown yet - even more, it previously was not known if this model separable at all. We present a precise definition of the subspace model, introducing the notion of simple components, show that the decomposition into simple components is unique and present an algorithm handling the decomposition task.


Irreducible Component Blind Source Separation Simple Component Irreducible Decomposition Simple Decomposition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Belouchrani, A., Abed-Meraim, K., Cardoso, J.-F., Moulines, E.: A blind source separation technique using second-order statistics. IEEE Transactions on Signal Processing 45(2), 434–444 (1997)CrossRefGoogle Scholar
  2. 2.
    Bunse-Gerstner, A., Byers, R., Mehrmann, V.: Numerical methods for simultaneous diagonalization. SIAM J. Matrix Anal. Appl. 14(4), 927–949 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Cardoso, J.-F., Souloumiac, A.: Jacobi angles for simultaneous diagonalization. SIAM J. Matrix Anal. Appl. 17(1), 161–164 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Gutch, H.W., Theis, F.J.: Independent subspace analysis is unique, given irreducibility. In: Davies, M.E., James, C.J., Abdallah, S.A., Plumbley, M.D. (eds.) ICA 2007. LNCS, vol. 4666, pp. 49–56. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  5. 5.
    Liu, W., Mandic, D.P., Cichocki, A.: Blind source extraction based on a linear predictor. IET Signal Process. 1(1), 29–34 (2007)CrossRefGoogle Scholar
  6. 6.
    Maehara, T., Murota, K.: Error-controlling algorithm for simultaneous block-diagonalization and its application to independent component analysis. JSIAM Letters (submitted)Google Scholar
  7. 7.
    Maehara, T., Murota, K.: Algorithm for error-controlled simultaneous block-diagonalization of matrices. Technical Report METR-2009-53 (December 2009)Google Scholar
  8. 8.
    Molgedey, L., Schuster, H.G.: Separation of a mixture of independent signals using time delayed correlations. Phys. Rev. Lett. 72(23), 3634–3637 (1994)CrossRefGoogle Scholar
  9. 9.
    Theis, F.J.: Towards a general independent subspace analysis. In: Proc. NIPS, pp. 1361–1368 (January 2006)Google Scholar
  10. 10.
    Tong, L., Soon, V.C., Huang, Y.-F., Liu, R.: AMUSE: a new blind identification algorithm. In: IEEE International Symposium on Circuits and Systems, vol. 3, pp. 1784–1787 (1990)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Department of Nonlinear DynamicsMax Planck Institute for Dynamics and Self-OrganizationGermany
  2. 2.Technical University of MunichGermany
  3. 3.University of TokyoJapan
  4. 4.Helmholtz-Institute NeuherbergGermany

Personalised recommendations