Charrelation Matrix Based ICA

Charrelation matrices are a generalization of the covariance matrix, encompassing statistical information beyond second order while maintaining a convenient 2-dimensional structure. In the context of ICA, charrelation matrices-based separation was recently shown to potentially attain superior performance over commonly used methods. However, this approach is strongly dependent on proper selection of the parameters (termed processing-points) which parameterize the charrelation matrices. In this work we derive a data-driven criterion for proper selection of the set of processing-points. The proposed criterion uses the available mixtures samples to quantify the resulting separation errors’ covariance matrix in terms of the processing points. Minimizing the trace of this matrix with respect to the processing points enables to optimize (asymptotically) the selection of these points, thereby yielding better separation results than other methods, as we demonstrate in simulation.