Near-optimal weighting in characteristic-function based ICA

In the context of Independent Component Analysis (ICA), we propose a near-optimal weighting scheme for the approximate joint diagonalization of empirical Hessians (second derivative matrices taken at selected "processing-points") of the observations\´ log-characteristic function. Our weighting scheme is based on the observation, that when the sources are nearly-separated, the covariance matrix of these empirical Hessians takes a convenient block-diagonal structure. We exploit this property to obtain reliable estimates of the blocks directly from the observed data, and use the recently proposed WEighted Diagonalization using Gauss itErations (WEDGE) to conveniently incorporate the weight matrices into the joint diagonalization estimation. Simulation results demonstrate the importance of proper weighting, especially for mitigating uncertainties in the selection of "processing points". As we show, the properly-weighted version can lead to a significant performance improvement, not only with respect to the unweighted version, but also with respect to a common benchmark like the popular JADE algorithm.