RobustICA algorithm for independent component analysis

RobustICA is based on the normalized kurtosis contrast function, which is optimized by a computationally efficient iterative technique. This technique computes algebraically the step size (adaption coefficient) globally optimizing the contrast in the search direction at each iteration. Any independent component with non-zero kurtosis can be extracted in this manner.

The present implementation performs the deflationary separation of statistically independent sources under the instantaneous linear mixture model. Full separation is achieved if at most one source has zero kurtosis.

Some advantages of RobustICA are:

• Real- and complex-valued signals are treated by exactly the same algorithm. Both type of source signals can be present simultaneously in a given mixture. Complex sources need not be circular. The mixing matrix coefficients may be real or complex, regardless of the source type.

• Prewhitening is not required, so that the performance limitations it imposes can be avoided. In particular, the absence of prewhitening improves asymptotic performance. In that case, sequential extraction (deflation) can be performed via linear regression.

• The algorithm can target sub-Gaussian or super-Gaussian sources in the order defined by a by a kurtosis-sign vector provided by the user. Full separation, as well as the consequent increase in complexity and estimation error, can be spared if the Gaussianity character of the source(s) of interest is known in advance.

• The optimal step-size technique provides some robustness to the presence of saddle points and spurious local extrema in the contrast function, which tend to appear when processing short data sizes.

• The method shows a very high convergence speed measured in terms of source extraction quality versus number of operations. In the real-valued two-signal case, the algorithm theoretically converges in a single iteration, even without prewhitening.

References

[1] V. Zarzoso and P. Comon, "Robust Independent Component Analysis by Iterative Maximization of the Kurtosis Contrast with Algebraic Optimal Step Size", IEEE Transactions on Neural Networks, Vol. 21, No. 2, February 2010, pp. 248-261. (721KB)

[2] V. Zarzoso and P. Comon, "Comparative Speed Analysis of FastICA", in: Proceedings ICA-2007, 7th International Conference on Independent Component Analysis and Signal Separation, London, UK, September 9-12, 2007, pp. 293-300. (336KB)

[3] V. Zarzoso, P. Comon and M. Kallel, "How Fast is FastICA?", in: Proceedings EUSIPCO-2006, XIV European Signal Processing Conference, Florence, Italy, September 4-8, 2006. (172KB)

What's new in Release 3:
• If required, the user can force the separating matrix to be real-valued. This is useful, e.g., when the mixing matrix is known to take real values but the separation is carried out in a complex domain (e.g., after Fourier transform).

• The calling syntax has been simplified by using a cell-array input argument.

• The code is now licensed under a Creative Commons Non-Commercial License (see Conditions of use for details).

What was new in Release 2 (Feb. 16, 2010):
• The optimal step-size computation has been refined (kurt_gradient_optstep.m function).

• Circular and noncircular complex sources are now included in the demonstration (robustica_demo.m function).

• For the sake of reproducible research, the code used to generate some of the results reported in reference [1] has been added to the package (robustica_tnn_fig3_sim.m and related functions).

Download and installation instructions:
• Download the zip-file by clicking on the above link.

• Extract the files into robustica_package directory.

• From Matlab's command line, set current directory to robustica_package.

• Type help robustica_package or doc robustica_package for details about the algorithm and the different functions contained in the package.

• Type robustica_demo to run a simple demo.

Conditions of use:
This is open-source code. Please, feel free to edit the M-files and modify them as you wish. It is only requested that original authorship be acknowledged and modifications be clearly indicated in the code (history section and elsewhere as appropriate).

If you use this package to generate results in your publications, please cite at least reference [1] above.


The RobustICA algorithm by Vicente Zarzoso and Pierre Comon is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Compatibility:
The package has been tested on Matlab 7.14.

Feedback:
Please, report any bugs, comments or suggestions to <>.