Non-linear adaptive systems

Lars Kai Hansen

Department of Informatics and Mathematical Modelling,
Building 321, Technical University of Denmark,
2800 Kongens Lyngby, Denmark

Abstract: Non-linearity is essential to some adaptive systems. So-called independent component analysis (ICA) for reconstruction of random source signals from linear mixtures, is a prominent example. Using linear systems it is only possible to recover the subspace spanned by the columns of the mixing matrix, while a broad class of non-linearities allow full recovery of both the unknown mixing matrix and the source signals, ie., blind signal separation. I will discuss recent progress in our understanding of the ICA problem based on mean field methods and linear response theory.