Blind identification problems with constraints

In many applications of independent component analysis (ICA) and blind source separation (BSS) the mixing or separating matrices have some special structure or some constraints are imposed for the matrices like symmetry, orthogonality, nonnegativity, sparseness and unit (or specified invariant norm) of the matrix. We present several algorithms and overview some known transformations which allows us to preserve such constraints. Especially, we propose algorithms for a blind identification problem with non-negativity constraints.

[1]  J. Nagy,et al.  Enforcing nonnegativity in image reconstruction algorithms , 2000, SPIE Optics + Photonics.

[2]  Mark D. Plumbley ADAPTIVE LATERAL INHIBITION FOR NON-NEGATIVE ICA , 2001 .

[3]  Patrik O. Hoyer,et al.  Non-negative sparse coding , 2002, Proceedings of the 12th IEEE Workshop on Neural Networks for Signal Processing.

[4]  Lars Kai Hansen,et al.  Blind detection of independent dynamic components , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[5]  Andrzej Cichocki,et al.  Adaptive blind signal and image processing , 2002 .

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

[7]  Shun-ichi Amari,et al.  On Some Extensions Of The Natural Gradient Algorithm , 2001 .

[8]  Alan Edelman,et al.  The Geometry of Algorithms with Orthogonality Constraints , 1998, SIAM J. Matrix Anal. Appl..

[9]  J. Pekar,et al.  GROUP ICA OF FUNCTIONAL MRI DATA: SEPARABILITY, STATIONARITY, AND INFERENCE , 2001 .

[10]  C. Byrne Block-iterative interior point optimization methods for image reconstruction from limited data , 2000 .

[11]  Sun-Yuan Kung,et al.  On gradient adaptation with unit-norm constraints , 2000, IEEE Trans. Signal Process..