LYCIA Toolbox - Algorithms
Algoritms for source generation
Second-order ICA algorithms
ICA by Maximization of non-Gaussianity
ICA algorithms using General methods: non-unitary demixing matrix
Fourth-order ICA algorithms
JADE
J. F. Cardoso and A. Souloumiac, "Blind beamforming for nongaussian signals," IEEE Trans. Signal Processing, vol. 140, no.6, pp. 362-370, 1993.
Brief introduction:
In the JADE algorithm, the separating matrix of complex ICA is found by joint diagonalisation of fourth-order cumulant matrices.
The mixtures are whitened first and joint diagonalisation of cumulant matrices allows the whole fourth-order cumulant set to be
processed with a computational efficiency similar to eigen-based techniques.
Parameters of the algorithm:
X: mixtures
Nem: number of eigen matrices used in the code, it could be m or m2 where m is the number of sources. The version of using m2
eigen matrices generally has better separating performance for large number of sources and it is also much more time-consuming.
CFPA
S. C. Douglas, "Fixed-point algorithms for the blind separation of arbitrary complex-valued non-Gaussian signal mixtures," EURASIP Journal on Applied Signal Processing, vol. 2007, no. 1, pp. 83-83, 2007.
Brief introduction:
This algorithm is also closely related to the circular complex FastICA algorithm. The normalized kurtosis function has been
used as the cost function. Different from other complex FastICA algorithms, this algorithm has a version that uses SUT to
whiten the data in order to deal with noncircular sources. It has been proved in the paper that the convergence performance
of this algorithm is mathematically identical to that of the real-valued FastICA algorithm with kurtosis contrast.
Parameters of the algorithm:
X: mixtures
Fixed point KM
H. Li and T. Adali, " A class of complex ICA algorithms based on the kurtosis cost function," IEEE Trans. Neural Networks, vol. 19, no. 3, pp. 408-420, March 2008.
Brief introduction:
This algorithm is a direct extension of real-valued FastICA algorithm to the complex domain using Wirtinger calculus. The kurtosis
function is used as the cost function to deal with circular and noncircular non-Gaussian signals. Equaling the separating matrix to
the gradient of kurtosis function yields the fixed-point update rule. It has been proved that the fixed-point KM has the same
convergence behavior as the real-valued FastICA algorithm.
Parameters of the algorithm:
X: mixtures
RobustICA
V. Zarzoso and P. Comon, "Robust Independent Component Analysis by Iterative Maximization of the Kurtosis Contrast with Algebraic Optimal Step Size," IEEE Trans. Neural Networks, vol. 21, no. 2, pp. 248-261, February 2010.
Brief introduction:
This algorithm performs exact line search optimization of the kurtosis contrast function to achieve deflationary ICA. The optimal step size leading to the global maximum of the contrast along the search direction is found among the roots of a fourth-degree polynomial and computed without iterations.
Parameters of the algorithm:
X: mixtures
kurtsign: source kurtosis signs (one element per source or empty). RobustICA maximizes absolute normalized kurtosis if element is zero; if this parameter is empty, the algorithm maximizes absolute normalized kurtosis for all sources.
prewhi: prewhitening via SVD of the observed data matrix. If this parameter is zero, then no prewhitening.
deftype: deflation type, 'o'rthogonalization or 'r'egression.
dimred: dimensionality reduction in regression if this parameter is not zero.
Wini: extracting vectors initialization for RobustICA iterative search. If this parameter is empty or not specified, identity matrix of suitable dimensions is used.
