Nonlinear blind source separation using kernel feature spaces

In this work we propose a kernel-based blind source separation (BSS) algorithm that can perform nonlinear BSS for general invertible nonlinearities. For our kTDSEP algorithm we have to go through four steps: (i) adapting to the intrinsic dimension of the data mapped to feature space F , (ii) finding an orthonormal basis of this submanifold, (iii) mapping the data into the subspace of F spanned by this orthonormal basis, and (iv) applying temporal decorrelation BSS (TDSEP) to the mapped data. After demixing we get a number of irrelevant components and the original sources. To find out which ones are the components of interest, we propose a criterion that allows to identify the original sources. The excellent performance of kTDSEP is demonstrated in experiments on nonlinearly mixed speech data.

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

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

[3]  Schuster,et al.  Separation of a mixture of independent signals using time delayed correlations. , 1994, Physical review letters.

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

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

[6]  Gustavo Deco,et al.  Linear redundancy reduction learning , 1995, Neural Networks.

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

[8]  A. Hyvärinen,et al.  Nonlinear Blind Source Separation by Self-Organizing Maps , 1996 .

[9]  Eric Moulines,et al.  A blind source separation technique using second-order statistics , 1997, IEEE Trans. Signal Process..

[10]  Juha Karhunen,et al.  A Maximum Likelihood Approach to Nonlinear Blind Source Separation , 1997, ICANN.

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

[12]  Juan K. Lin,et al.  Faithful Representation of Separable Distributions , 1997, Neural Computation.

[13]  Andreas Ziehe,et al.  TDSEP — an efficient algorithm for blind separation using time structure , 1998 .

[14]  Andrzej Cichocki,et al.  Information-theoretic approach to blind separation of sources in non-linear mixture , 1998, Signal Process..

[15]  Aapo Hyvärinen,et al.  Nonlinear independent component analysis: Existence and uniqueness results , 1999, Neural Networks.

[16]  Ali Mansour,et al.  Blind Separation of Sources , 1999 .

[17]  Christian Jutten,et al.  Source separation in post-nonlinear mixtures , 1999, IEEE Trans. Signal Process..

[18]  Pei Ling Lai,et al.  Ica Using Kernel Canonical Correlation Analysis , 2000 .

[19]  Vladimir N. Vapnik,et al.  The Nature of Statistical Learning Theory , 2000, Statistics for Engineering and Information Science.

[20]  Juha Karhunen,et al.  Nonlinear Independent Component Analysis Using Ensemble Learning: Experiments and Discussion , 2000 .

[21]  Gunnar Rätsch,et al.  An introduction to kernel-based learning algorithms , 2001, IEEE Trans. Neural Networks.

[22]  T. Sejnowski,et al.  Separation of post-nonlinear mixtures using ACE and temporal decorrelation , 2001 .

[23]  Dustin Boswell,et al.  Introduction to Support Vector Machines , 2002 .

[24]  Constance de Koning,et al.  Editors , 2003, Annals of Emergency Medicine.