Linearization identification and an application to BSS using a SOM

The one-dimensional functional equation g(y(t)) = cg(z(t)) with known functions y and z and constant c is considered. The indeterminacies are calculated, and an algorithm for approximating g given y and z at finitely many time instants is proposed. This linearization identification algorithm is applied to the postnonlinear blind source separation (BSS) problem in the case of independent sources with bounded densities. A self-organizing map (SOM) is used to approximate the boundary, and the postnonlinearity estimation in this multivariate case is reduced to the one-dimensional functional equation from above.