A Novel Grid Occupancy Criterion for Independent Component Analysis

Transform each coordinate of the realizations of several random variables (RVs) by the distribution function of the corresponding RV and partition the range space into a uniform grid. The expected number of occupied grid-boxes will be greatest when these RVs are independent. Based on this fact, we propose a novel measure of independence named grid occupancy (GO). We also address the problem of how to make optimum selection of the parameters in GO, i.e., the number of observations and the number of quantization levels. In addition, we apply GO to independent component analysis (ICA). The GO based ICA algorithm can separate signals with arbitrary continuous distributions and favors digital hardware implementation.