On the spurious solutions of the Fastica algorithm

The present contribution deals with the statistical tool of Independent Component Analysis (ICA). The focus is on Fas-tICA, arguably the most popular algorithm in the domain of ICA. Despite its success, it is observed that FastICA occasionally yields outcomes that do not correspond to any solutions of ICA. These outcomes are called spurious solutions. In this work, we give a thorough and rigorous investigation of the spurious solutions of FastICA. We characterize various sets of interest and show that the kurtosis-based FastICA is theoretically free of spurious solutions. Examples are given, showing that in certain scenarios, popular nonlinearities such as “Gauss” or “tanh” systematically yield spurious solutions, whereas only “kurtosis” may give reliable results.