Nonlinear Independent Component Analysis using Generalised Polynomial Neural Network

In this paper, a new polynomial neuron-based network is proposed to tackle the problem of nonlinear Independent Component Analysis (ICA). We extend our research from a recently presented mono-nonlinearity mixture where a linear mixing matrix is sandwiched between two mutually inverse nonlinearities to a so-called multi-nonlinearity constrained mixing model. Our aim is to generalize the mono-nonlinearity mixing system to the situation that different nonlinearities are now allowed to be used for sources. Meanwhile, the theory of Series Reversion is adopted with the neural network demixer to make use of the a priori ‘inverse’ information between two layers of nonlinearities. The parameter learning algorithm for this special polynomial network demixer is also presented. Simulations have been carried out to verify the efficacy of the proposed approach. We demonstrate that the proposed network can successfully recover the original source signals in a blind mode under nonlinear mixing conditions. Key-Words: Independent Component Analysis, Blind Signal Separation, Series Reversion, Neural Network.