Nonlinear approaches to independent component analysis

Recently, there has been a great interest in statistical models for learning data representations. ii popular method for this task is Independent Component Analysis (ICA) which has been successfully applied for the blind separation of mixed sounds and the analysis of biomedical signals. ICA relies on strong assumptions such as the linear mixing model, the requirement that the number of sensors are equal of greater than the number of sources, and that there is no additive noise. Some of the constraints are violated in practical applications and in order to relax the assumptions new methods need to be developed which involve nonlinear unmixing or inference solutions. In this paper, Ne summarize some techniques that involve nonlinear ICA solutions. Tao approaches are presented to tackle the nonlinear mixing case, and nonlinear ICA solutions are summarized for overcomplete representation as well as additive noise problems.