In many real world situations the linear assumption is an approximation of nonlinear phenomena. For several situations the linear assumption may lead to incorrect solutions. Therefore the goal in this chapter is to formulate an ICA framework that is able to separate nonlinear mixing models. Researchers have very recently started addressing the ICA formulation to nonlinear mixing models (Burel, 1992; Hermann and Yang, 1996; Lee et al., 1997c; Lin and Cowan, 1997; Pajunen, 1996; Taleb and Jutten, 1997; Yang et al., 1997) The proposed nonlinear ICA methods can be roughly divided into two classes of approaches. The first class of methods is an obvious extension to the linear ICA model where nonlinear mixing models are added to the linear model and the task is to find the inverse of the linear model as well as the inverse of the nonlinear model (Burel, 1992; Lee et al., 1997c; Taleb and Jutten, 1997; Yang et al., 1997). The nonlinearities are often parameterized allowing limited flexibility. More recently, Hochreiter and Schmidhuber (1998) have proposed low complexity coding and decoding approaches for nonlinear ICA. The second class of methods uses self-organizing-maps (SOM) to extract nonlinear features in the data (Hermann and Yang, 1996; Lin and Cowan, 1997; Pajunen, 1996) Their approach is more flexible and to some extent parameter-free which allows greater freedom of nonlinear representation.
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