Joint Approximation Diagonalization of Eigen-matrices

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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.[1] 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[edit]

Let denote an observed data matrix whose columns correspond to observations of -variate mixed vectors. It is assumed that is prewhitened, that is, its rows have a sample mean equaling zero and a sample covariance is the dimensional identity matrix, that is,

.

Applying JADE to entails

  1. computing fourth-order cumulants of and then
  2. optimizing a contrast function to obtain a rotation matrix

to estimate the source components given by the rows of the dimensional matrix .[2]

References[edit]

  1. ^ Cardoso, Jean-François; Souloumiac, Antoine (1993). "Blind beamforming for non-Gaussian signals". IEE Proceedings F (Radar and Signal Processing). 140 (6): 362–370.
  2. ^ Cardoso, Jean-François (Jan 1999). "High-order contrasts for independent component analysis". Neural Computation. 11 (1): 157–192. doi:10.1162/089976699300016863.