FastICA Algorithm: Five Criteria for the Optimal Choice of the Nonlinearity Function

Using an infinite sample, the contrast function and the FastICA algorithm are deterministic. In the practical case, we have only a finite sample. Then the contrast function and the FastICA algorithm become estimators of the deterministic case. This paper provides a unified study of the deflation FastICA algorithm assuming a finite or an infinite sample. We consider four random probability distributions based on the finite sample, and construct four FastICA estimators. We show that under mild conditions, each of these estimators are equal to a local minimizer of the contrast function with respect to the underlying random probability distribution. Making use of the existing results of M-estimators, we give a rigorous analysis of the asymptotic errors of FastICA estimators. We derive five criteria for the optimal choice of the nonlinearity function.