Nonparametric Independent Component Analysis for Circular Complex Variables

A new consistent objective function for nonparametric complex independent component analysis (ICA) is proposed where the complex variables are restricted to be circular, or radially symmetric. This objective function is derived using an order statistics based density estimator which orders the complex data by their absolute values. The objective function is unconditional to the source distribution other than the circularity and it measures the statistical independence directly from the data. Using this objective function, a nonparametric complex independent component analysis algorithm can be derived. Also, the generalization of this objective function allows it to be combined with other algorithms to increase their separation performances. Experiments demonstrate the usefulness of the new objective function.