We study and derive a method to speed up kurtosis-based FastICA in presence of information redundancy, i.e., for large samples. It consists in randomly decimating the data set as more as possible while preserving the quality of the reconstructed signals. By performing an analysis of the kurtosis estimator, we find the maximum reduction rate which guarantees a narrow confidence interval of such estimator with high confidence level. Such a rate depends on a parameter β easily computed a priori

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... bining together the fourth and the eighth norms of the observations. Extensive simulations have been done on different sets of real world signals. They show that actually the sample size reduction is very high, preserves the quality of the decomposition and impressively speeds up FastICA. On the other hand, the simulations also show that, decimating data more than the rate fixed by β, the decomposition ability of FastICA is compromised, thus validating the reliability of the parameter β. We are confident that our method will follow to better approach real time applications.