An Improved Natural Gradient ICA Algorithm Based on Lie Group Invariance

This paper proposes an improved natural gradient ICA (independent component analysis) algorithm based on the Riemannian structure of parameter space. The new algorithm introduces a scaling factor which makes the absolute value of the determinant of parameter matrix equal to one in the whole learning process. Therefore, the training process is faster and stable by restricting the drastic change of parameter matrix. In addition, the general criterion function is simplified by the scaling factor. In simulation experiment, we compare three algorithms including ordinary gradient ICA algorithm, natural gradient ICA algorithm and improved natural gradient ICA algorithm. Comparing the new improved natural gradient ICA with the natural gradient ICA, the mean relative error of restored signals is decreased 38.7%. The results show that the latter is better in restored-signal precision and convergence speed