Semi-invariant function of Jacobi algorithm in independent component analysis

It has been known that several Jacobi algorithms (e.g. JADE, MaxKurt, EML, and so on) are useful in independent component analysis (ICA). This work shows that the sum of 4th order (iijj-) cumulants over all the pairs of components is a "semi-invariant" function of such Jacobi algorithms. Then we prove that MaxKurt algorithm converges monotonically without loss to a local minimum of the semi-invariant function, which is consistent with the result obtained by the symmetrical maximization of kurtoses. In addition, a new algorithm combining EML and JADE is proposed. The EML-JADE algorithm not only uses both maximization and minimization of kurtoses suitably like EML but also utilizes JADE in the cases where super- and sub-gaussian sources are highly mixed.