A new algorithm for independent component analysis with or without constraints

A new algorithm is developed for independent component analysis (ICA) with or without constraints on the mixing matrix or sources. The algorithm is based on the criterion of Joint Approximate Diagonalization of Eigen-matrices (JADE). We propose a column-wise processing approach to perform joint diagonalization of the cumulant (eigen-) matrices. We utilize the unitary property of diagonalizing matrix U and achieve decoupling of its columns via orthogonal projections. We propose a method called Alternating Eigen-search (AE) to maximize the JADE criterion with respect to one column of U at a time. The method is extended to the case in which there are application-dependent quadratic constraints imposed on the mixing matrix or sources, resulting in the so-called constrained ICA. Example results are provided to demonstrate the effectiveness and applicability of the algorithm.

[1]  Peter Lancaster,et al.  The theory of matrices , 1969 .

[2]  S. Haykin,et al.  Adaptive Filter Theory , 1986 .

[3]  Jerry M. Mendel,et al.  Tutorial on higher-order statistics (spectra) in signal processing and system theory: theoretical results and some applications , 1991, Proc. IEEE.

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

[5]  C. L. Nikias,et al.  Higher-order spectra analysis : a nonlinear signal processing framework , 1993 .

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

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

[8]  M. Wax,et al.  A least-squares approach to joint diagonalization , 1997, IEEE Signal Processing Letters.

[9]  Jerry M. Mendel,et al.  Applications of cumulants to array processing. III. Blind beamforming for coherent signals , 1997, IEEE Trans. Signal Process..

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

[11]  E. Moreau,et al.  A generalized ICA algorithm , 2000, IEEE Signal Processing Letters.

[12]  Erkki Oja,et al.  Independent component analysis: algorithms and applications , 2000, Neural Networks.

[13]  Erkki Oja,et al.  Independent component approach to the analysis of EEG and MEG recordings , 2000, IEEE Transactions on Biomedical Engineering.

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

[15]  Joos Vandewalle,et al.  Independent component analysis and (simultaneous) third-order tensor diagonalization , 2001, IEEE Trans. Signal Process..

[16]  Eric Moreau,et al.  A generalization of joint-diagonalization criteria for source separation , 2001, IEEE Trans. Signal Process..

[17]  Tzyy-Ping Jung,et al.  Imaging brain dynamics using independent component analysis , 2001, Proc. IEEE.

[18]  Xiao Ma,et al.  Design of unitary precoders for ISI channels , 2002, 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing.