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The fastICA method is a popular dimension reduction technique used to revealpatterns in data. Here we show both theoretically and in practice that theapproximations used in fastICA can result in patterns not being successfullyrecognised. We demonstrate this problem using a two-dimensional example where aclear structure is immediately visible to the naked eye, but where theprojection chosen by fastICA fails to reveal this structure. This implies thatcare is needed when applying fastICA. We discuss how the problem arises and howit is intrinsically connected to the approximations that form the basis of thecomputational efficiency of fastICA.

On the Estimation of Entropy in the FastICA Algorithm