Deflation-Based FastICA With Adaptive Choices of Nonlinearities

Deflation-based FastICA is a popular method for independent component analysis. In the standard deflation-based approach the row vectors of the unmixing matrix are extracted one after another always using the same nonlinearities. In practice the user has to choose the nonlinearities and the efficiency and robustness of the estimation procedure then strongly depends on this choice as well as on the order in which the components are extracted. In this paper we propose a novel adaptive two-stage deflation-based FastICA algorithm that (i) allows one to use different nonlinearities for different components and (ii) optimizes the order in which the components are extracted. Based on a consistent preliminary unmixing matrix estimate and our theoretical results, the algorithm selects in an optimal way the order and the nonlinearities for each component from a finite set of candidates specified by the user. It is also shown that, for each component, the best possible nonlinearity is obtained by using the log-density function. The resulting ICA estimate is affine equivariant with a known asymptotic distribution. The excellent performance of the new procedure is shown with asymptotic efficiency and finite-sample simulation studies.

[1]  Jean-Francois Cardoso,et al.  Source separation using higher order moments , 1989, International Conference on Acoustics, Speech, and Signal Processing,.

[2]  Esa Ollila.  On the robustness of the deflation-based FastICA estimator , 2009, 2009 IEEE/SP 15th Workshop on Statistical Signal Processing.

[3]  Aapo Hyvärinen,et al.  Fast and robust fixed-point algorithms for independent component analysis , 1999, IEEE Trans. Neural Networks.

[4]  Klaus Nordhausen,et al.  A New Performance Index for ICA: Properties, Computation and Asymptotic Analysis , 2010, LVA/ICA.

[5]  D. Chakrabarti,et al.  A fast fixed - point algorithm for independent component analysis , 1997 .

[6]  Esa Ollila,et al.  The Deflation-Based FastICA Estimator: Statistical Analysis Revisited , 2010, IEEE Transactions on Signal Processing.

[7]  Klaus Nordhausen,et al.  Deflation-based FastICA reloaded , 2011, 2011 19th European Signal Processing Conference.

[8]  Pauliina Ilmonen,et al.  Characteristics of multivariate distributions and the invariant coordinate system , 2010 .

[9]  A. Hyvärinen,et al.  One-unit contrast functions for independent component analysis: a statistical analysis , 1997 .

[10]  Klaus Nordhausen,et al.  Fast equivariant JADE , 2013, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing.

[11]  P. Tichavský,et al.  Efficient variant of algorithm fastica for independent component analysis attaining the cramer-RAO lower bound , 2005, IEEE/SP 13th Workshop on Statistical Signal Processing, 2005.

[12]  Seungjin Choi,et al.  Independent Component Analysis , 2009, Handbook of Natural Computing.

[13]  Michael I. Jordan,et al.  Kernel independent component analysis , 2003, 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)..

[14]  Erkki Oja,et al.  Efficient Variant of Algorithm FastICA for Independent Component Analysis Attaining the CramÉr-Rao Lower Bound , 2006, IEEE Transactions on Neural Networks.

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

[16]  J. Cardoso,et al.  Blind beamforming for non-gaussian signals , 1993 .