Jutten-Hérault algorithm

The pioneering work in [80] was inspired by neural networks. Their algorithm was based on canceling the non-linear cross-correlations, see Section 4.3.3. The non-diagonal terms of the matrix ${\bf W}$ are updated according to

$$\Delta {\bf W}_{ij}\propto g_1(y_i)g_2(y_j), \mbox{for }i\neq j$$ (33)

where g₁ and g₂ are some odd non-linear functions, and the y_iare computed at every iteration as ${\bf y}=({\bf I}+{\bf W})^{-1}{\bf x}$. The diagonal terms ${\bf W}_{ii}$ are set to zero. The y_i then give, after convergence, estimates of the independent components. Unfortunately, the algorithm converges only under rather severe restrictions (see [40]).