Low-rank signal approximations with reduced error dispersion

Low-rank representations of multivariate signals are useful in a wide variety of applications such as data compression, feature extraction and noise filtering. Several matrix decomposition techniques like principal component analysis and independent component analysis have been proposed so far for reduced-rank signal representation. However, these methods have no effect on the error dispersion across observations, which may lead to poor representation of some input variables. To render a more uniform description of the observed data, this work puts forth a novel technique for reduced error dispersion (RED) based on a p-norm minimization criterion, with p > 1. The RED criterion is minimized by an iterative algorithm alternating between a gradient descent update and a least squares (LS) step via singular value decomposition. Links with existing weighted LS approaches are also established. A simulation study demonstrates the satisfactory convergence of the proposed algorithm and its ability to approximate the observed data with improved reconstruction error uniformity at a negligible impact on the average error.