Soft-LOST: EM on a Mixture of Oriented Lines

  • Paul D. O’Grady
  • Barak A. Pearlmutter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3195)


Robust clustering of data into overlapping linear subspaces is a common problem. Here we consider one-dimensional subspaces that cross the origin. This problem arises in blind source separation, where the subspaces correspond directly to columns of a mixing matrix. We present an algorithm that identifies these subspaces using an EM procedure, where the E-step calculates posterior probabilities assigning data points to lines and M-step repositions the lines to match the points assigned to them. This method, combined with a transformation into a sparse domain and an L 1-norm optimisation, constitutes a blind source separation algorithm for the under-determined case.


Attenuation Covariance 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Paul D. O’Grady
    • 1
  • Barak A. Pearlmutter
    • 1
  1. 1.Hamilton InstituteNational University of IrelandMaynooth, Co. KildareIreland

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