Talk:FastICA

Error in formula?
The cited paper I ("Independent component analysis: Algorithms and applications") includes the following formula:

$$\mathbf{w}^+ = E\{\mathbf{x} g(\mathbf{w}^T \mathbf{x})\} - E\{g'(\mathbf{w}^T \mathbf{x})\} \mathbf{w}$$

This formula seems to me to be in error ($$\mathbf{x}$$ is a column vector; the dimensions don't work out). The current version of the article has this formula:

$$\mathbf{w}^+ \leftarrow E\left\{\mathbf{X} g(\mathbf{w}^T \mathbf{X})^T\right\} - E\left\{g'(\mathbf{w}^T \mathbf{X})\right\}\mathbf{w}$$

I believe this is also in error (the first term is transposed relative to the second term). I believe the correct version, as implemented in [scikit-learn's implementation of FastICA] is as follows:

$$\mathbf{w}^+ = E\{g(\mathbf{w}^T\mathbf{x}) \mathbf{x}^T\} - E\{g'(\mathbf{w}^T \mathbf{x})\} \mathbf{w}$$

Does this seem right? Can I cite the source code as a reference to update the formula? rdl381 (talk) 15:59, 19 January 2024 (UTC)