JADE (ICA)

Joint Approximation Diagonalization of Eigen-matrices (JADE) is an algorithm for independent component analysis that separates observed mixed signals into latent source signals by exploiting fourth order moments. The fourth order moments are a measure of non-Gaussianity, which is used as a proxy for defining independence between the source signals. The motivation for this measure is that Gaussian distributions possess zero excess kurtosis, and with non-Gaussianity being a canonical assumption of ICA, JADE seeks an orthogonal rotation of the observed mixed vectors to estimate source vectors which possess high values of excess kurtosis.

Algorithm

Let $\mathbf = (x_) \in \mathbb^$ denote an observed data matrix whose $n$ columns correspond to observations of $m$-variate mixed vectors. It is assumed that $\mathbf$ is ''prewhitened'', that is, its rows have a sample mean equaling zero and a sample covariance is the $m \times m$ dimensional identity matrix, that is,

Applying JADE to $\mathbf$ entails
# computing ''fourth-order cumulants'' of $\mathbf$ and then
# optimizing a ''contrast function'' to obtain a $m \times m$ rotation matrix $O$
to estimate the source components given by the rows of the $m \times n$ dimensional matrix $\mathbf := \mathbf^ \mathbf$.

References

Computational statistics

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