In this paper some alternative Riemannian metrics are defined on the parameter space of non-square matrices, corresponding to various translations defined therein. Such metrics allow the authors to derive novel learning rules for two ICA based algorithms for over-determined blind source separation (BSS), which tries to separate less sources from more sensors. Computer simulations show a significant improvement of the convergence speed when second-order translations are employed in contrast to their first-order counterparts, extending known results for complete BSS