Nonlinear Independent Component Analysis by Self-Organizing Maps

Linear Independent Component Analysis considers the problem of finding a linear transformation that makes the components of the output vector statistically independent. This can be applied to blind source separation, where the input data consist of unknown linear mixtures of unknown independent source signals. The original source signals can be recovered from their mixtures using the assumption that they are statistically independent. More generally we can consider nonlinear mappings that make the components of the output vectors independent. We show that such a mapping can be approximately realized using self-organizing maps with rectangular map topology. We apply these mappings to the separation of nonlinear mixtures of sub-Gaussian sources