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