Equi-convergence Algorithm for Blind Separation of Sources with Arbitrary Distributions

This paper presents practical implementation of the equiconvergent learning algorithm for blind source separation. The equiconvergent algorithm [4] has favorite properties such as isotropic convergence and universal convergence, but it requires to estimate unknown activation functions and certain unknown statistics of source signals. The estimation of such activation functions and statistics becomes critical in realizing the equi-convergent algorithm. It is the purpose of this paper to develop a new approach to estimate the activation functions adaptively for blind source separation. We propose the exponential type family as a model for probability density functions. A method of constructing an exponential family from the activation (score) functions is proposed. Then, a learning rule based on the maximum likelihood is derived to update the parameters in the exponential family. The learning rule is compatible with minimization of mutual information for training demixing models. Finally, computer simulations are given to demonstrate the effectiveness and validity of the proposed approach.

[1]  Liqing Zhang,et al.  Natural gradient algorithm for blind separation of overdetermined mixture with additive noise , 1999, IEEE Signal Processing Letters.

[2]  Hagai Attias,et al.  Independent Factor Analysis , 1999, Neural Computation.

[3]  Andrzej Cichocki,et al.  Robust neural networks with on-line learning for blind identification and blind separation of sources , 1996 .

[4]  Andrzej Cichocki,et al.  A New Learning Algorithm for Blind Signal Separation , 1995, NIPS.

[5]  Shun-ichi Amari,et al.  Natural Gradient Works Efficiently in Learning , 1998, Neural Computation.

[6]  Jean-François Cardoso,et al.  Equivariant adaptive source separation , 1996, IEEE Trans. Signal Process..

[7]  Erkki Oja,et al.  Signal Separation by Nonlinear Hebbian Learning , 1995 .

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

[9]  Shun-ichi Amari,et al.  Blind source separation-semiparametric statistical approach , 1997, IEEE Trans. Signal Process..

[10]  S. Amari,et al.  Estimating Functions in Semiparametric Statistical Models , 1997 .

[11]  S. Amari,et al.  Multichannel blind separation and deconvolution of sources with arbitrary distributions , 1997, Neural Networks for Signal Processing VII. Proceedings of the 1997 IEEE Signal Processing Society Workshop.

[12]  Shun-ichi Amari,et al.  Differential-geometrical methods in statistics , 1985 .

[13]  Andrzej Cichocki,et al.  Stability Analysis of Learning Algorithms for Blind Source Separation , 1997, Neural Networks.

[14]  Terrence J. Sejnowski,et al.  Independent Component Analysis Using an Extended Infomax Algorithm for Mixed Subgaussian and Supergaussian Sources , 1999, Neural Computation.

[15]  Christian Jutten,et al.  Blind separation of sources, part I: An adaptive algorithm based on neuromimetic architecture , 1991, Signal Process..

[16]  Shun-ichi Amari,et al.  Methods of information geometry , 2000 .

[17]  S. Amari,et al.  Information geometry of estimating functions in semi-parametric statistical models , 1997 .

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