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)