Alternative Derivation of FastICA With Novel Power Iteration Algorithm

The widely used fixed-point FastICA algorithm has been derived and motivated as being an approximate Newton-Raphson (NR) algorithm. In the original derivation, the Lagrangian multiplier is treated as a constant and an ad hoc approximation is used for Jacobian matrix in the NR update. In this letter, we provide an alternative derivation of the FastICA algorithm without approximation. We show that any solution to the FastICA algorithm is a solution to the exact NR algorithm as well. In addition, we propose a novel power iteration algorithm for FastICA which is remarkably more stable than the fixed-point algorithm, when the sample size is not orders of magnitudes larger than the dimension. Our proposed algorithm can be run on parallel computing nodes.