Parametric independent component analysis for stable distributions

Independent Component Analysis (ICA) is a method for blind source separation of a multivariate dataset that transforms observations to new statistically independent linear forms. Infinite variance of non-Gaussian α-stable distributions makes algorithms like ICA non-appropriate for these distributions. In this note, we propose an algorithm which computes mixing matrix of ICA, in a parametric subclass of α -stable distributions.

[1]  Messaoud Benidir,et al.  Blind separation of impulsive alpha-stable sources using minimum dispersion criterion , 2005, IEEE Signal Processing Letters.

[2]  Terrence J. Sejnowski,et al.  An Information-Maximization Approach to Blind Separation and Blind Deconvolution , 1995, Neural Computation.

[3]  Yannick Deville,et al.  Blind separation of piecewise stationary non-Gaussian sources , 2009, Signal Process..

[4]  Preben Kidmose,et al.  Blind separation of heavy tail signals , 2001 .

[5]  D. Applebaum.  Stable non-Gaussian random processes , 1995, The Mathematical Gazette.

[6]  K. Knight.  Stable Non-Gaussian Random Processes Gennady Samorodnitsky and Murad S. Taqqu Chapman and Hall, 1994 , 1997, Econometric Theory.

[7]  Aapo Hyvärinen,et al.  A Fast Fixed-Point Algorithm for Independent Component Analysis , 1997, Neural Computation.

[8]  James V. Stone.  Blind Source Separation Using Temporal Predictability , 2001, Neural Computation.

[9]  J. McCulloch,et al.  Estimation of stable spectral measures , 2001 .

[10]  Jean-Franois Cardoso.  High-Order Contrasts for Independent Component Analysis , 1999, Neural Computation.

[11]  Mohamed Sahmoudi,et al.  Blind Separation of Heavy-Tailed Signals Using Normalized Statistics , 2004, ICA.

[12]  E. Oja,et al.  Independent Component Analysis , 2013 .

[13]  Andrzej Cichocki,et al.  Adaptive Blind Signal and Image Processing - Learning Algorithms and Applications , 2002 .

[14]  Rui Li,et al.  Data Mining with Independent Component Analysis , 2006, 2006 6th World Congress on Intelligent Control and Automation.

[15]  Pierre Comon,et al.  Independent component analysis, A new concept? , 1994, Signal Process..

[16]  R. Penrose.  A Generalized inverse for matrices , 1955 .