FastICA

FastICA is an efficient and popular algorithm for independent component analysis invented by Aapo Hyvärinen at Helsinki University of Technology. The algorithm is based on a fixed-point iteration scheme maximizing non-Gaussianity as a measure of statistical independence. It can be also derived as an approximative Newton iteration.

Algorithm

FastICA for one unit

The iterative algorithm finds the direction for the weight vector $mathbf\{w\}$maximizing the non-Gaussianity of the projection $mathbf\{w\}^T\; mathbf\{x\}$for the data $mathbf\{x\}$.The function $g(cdot)$ is the derivative of a nonquadratic nonlinearity.

# Choose an initial weight vector $mathbf\{w\}$
# Let $mathbf\{w\}^+\; leftarrow\; Eleft\{mathbf\{x\}\; g(mathbf\{w\}^T\; mathbf\{x\})\; ight\}\; -\; Eleft\{g\text{'}(mathbf\{w\}^T\; mathbf\{x\})\; ight\}mathbf\{w\}$
# Let $mathbf\{w\}\; leftarrow\; mathbf\{w\}^+\; /\; |mathbf\{w\}^+|$
# If not converged, go back to 2

See also

* Independent component analysis (ICA)
* Unsupervised learning
* Machine learning

External links

* [http://www.cis.hut.fi/projects/ica/fastica/ FastICA package for Matlab]
* [http://cran.r-project.org/src/contrib/Descriptions/fastICA.html fastICA package] in R programming language

References

Hyvärinen,A (1999). Fast and Robust Fixed-Point Algorithms for Independent Component Analysis. IEEE Transactions on Neural Networks, 10(3),626-634.