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. For example $g(t)$ could be the derivative of $f(t)=t^4$.

1. Choose an initial weight vector $\mathbf{w}$
2. Let $\mathbf{w}^+ \leftarrow E\left\{\mathbf{x} g(\mathbf{w}^T \mathbf{x})\right\} - E\left\{g'(\mathbf{w}^T \mathbf{x})\right\}\mathbf{w}$
3. Let $\mathbf{w} \leftarrow \mathbf{w}^+ / \|\mathbf{w}^+\|$
4. If not converged, go back to 2

See also

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

External links

• FastICA package for Matlab or Octave
• fastICA package in R programming language
• FastICA in Java on SourceForge
• FastICA in Java in RapidMiner.

References

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