FastICA

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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.

1 Algorithm
- 1.1 FastICA for one unit
2 See also
3 External links
4 References

[edit] Algorithm

[edit] 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 $\mathbf{w}^+ \leftarrow E\left\{\mathbf{x} g(\mathbf{w}^T \mathbf{x})\right\} - E\left\{g'(\mathbf{w}^T \mathbf{x})\right\}\mathbf{w}$
Let $\mathbf{w} \leftarrow \mathbf{w}^+ / \|\mathbf{w}^+\|$
If not converged, go back to 2