Rotation of Eofs by the Independent Component Analysis: Towards a Solution of the Mixing Problem in the Decomposition of Geophysical Time Series

The Independent Component Analysis (ICA) is a recently developed technique for component extraction. This new method requires the statistical independence of the extracted components—a stronger constraint that uses higher-order statistics—instead of the classical decorrelation (in the sense of ‘‘no correlation’’), which is a weaker constraint that uses only second-order statistics. This technique has been used recently for the analysis of geophysical time series with the goal of investigating the causes of variability in observed data (i.e., exploratory approach). The authors demonstrate with a data simulation experiment that, if initialized with a Principal Component Analysis (PCA), the ICA performs a rotation of the classical PCA (or EOF) solution. This experiment is conducted using a synthetic dataset, where the correct answer is known, to more clearly illustrate and understand the behavior of the more familiar PCA and less familiar ICA. This rotation uses no localization criterion like other rotation techniques; only the generalization of decorrelation into full statistical independence is used. This rotation of the PCA solution seems to be able to avoid the tendency of PCA to mix several components, even when the signal is just their linear sum.