Joint Approximation Diagonalization of Eigen-matrices

Joint Approximation Diagonalisation of Eigenmatrices (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 proxy measure for non-Gaussianity, which is used for defining independence between the source signals.

Algorithm

Let $\mathbf {X} =(x_{ij})\in \mathbb {R} ^{n\times m}$ denote an observed data matrix whose $n$ rows correspond to observations of $m$-variate mixed vectors. It is assumed that $\mathbf {X} \in \mathbb {R} ^{n\times m}$ is prewhitenend, that is, the sample of mean of each column is zero and the sample covariance of its rows is the $m\times m$ dimensional identity matrix, that is,

${\frac {1}{n}}\sum _{i=1}^{n}x_{ij}=0\quad {\text{and}}\quad {\frac {1}{n}}\mathbf {X} ^{\prime }{\mathbf {X} }=\mathbf {I} _{m}$.