Technical Report on Separation Methods for Nonlinear Mixtures
Christian Jutten, Almeida Karhunen J, Stefan Harmeling · MPG.PuRe (Max Planck Society) · 2003
This subproject considered ICA and BSS problems for nonlinear data models.In that case, ICA is characterized by severe indeterminacies, which makes the BSS problem ill-posed.Hence some kind of regularization is necessary for actually achieving solutions which can be interpreted as underlying sources.The problem of regularization has been analyzed from different perspectives and resulted in powerful methods.For example, explicit constraints on the model class are used in the case of post-nonlinear mixtures, where the nonlinearity is modeled as a component-wise distortion of linear mixtures.More implicit constraints are implemented in kernelbased methods like kTDSEP, where the choice of the kernel parameters regularizes the complexity of the nonlinearities.Also, exploiting prior information on the sources, for example bounded or temporally correlated sources, reduces the indeterminacies in the solutions and leads to simplified algorithms.Another promising method consists in regularizing the solution using a fully Bayesian variational ensemble learning approach.It tries to find the sources and the mapping that have most probably generated the observed data given the prior.The ensemble learning method allows nonlinear source separation for problems of realistic size, and it can be easily extended in various directions.It has been argued that regularization based on an assumption of smoothness of the mixture could overcome the ill-posedness of nonlinear BSS.Although it is still a matter of debate under what exact conditions this is true, several examples of successful source recovery through the MISEP method, using smoothness for regularization, have been presented.Last but not least, there has been a high degree of cooperation among the partners to compare the results and to promote combined approaches.