Joint Approximation Diagonalization of Eigen matrices - Alchetron, the free social encyclopedia

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 X = ( x i j ) ∈ R m × n denote an observed data matrix whose n columns correspond to observations of m -variate mixed vectors. It is assumed that X is prewhitenend, that is, its rows have a sample mean equaling zero and a sample covariance is the m × m dimensional identity matrix, that is,

1 n ∑ j = 1 n x i j = 0 and 1 n X X ′ = I m .

Applying JADE to X entails

computing fourth-order cumulants of X and then
optimizing a contrast function to obtain a m × m rotation matrix O

to estimate the source components given by the rows of the m × n dimensional matrix Z := O − 1 X .

References

Joint Approximation Diagonalization of Eigen-matrices Wikipedia

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