Comparing Independent Component Analysis and the Parafac model for artificial multi-subject fMRI data

Recently, Beckmann and Smith (2005) compared a three-way extension of Independent Component Analysis (ICA) and the Parafac model, as applied to artificial multi-subject fMRI data (voxels × scans × subjects). They concluded that the ICA approach yields more accurate estimates of the underlying signal sources and results in less interference between the different sources compared to the Parafac estimates. Moreover, the ICA approach is more robust against overfitting and its computational load is much less than Parafac. In this paper, we offer detailed explanations of the differences between Parafac and the ICA approach and show that the distinction between second-order statistics versus higher-order statistics does not apply to Parafac versus ICA. Using the data of Beckmann and Smith (2005), we show that Parafac performs as well as the ICA approach if the correct number of signal sources is chosen, which is possible by considering Parafac fit values. Moreover, if the fMRI spatial activity maps are well-overlapping, then the ICA approach does not find the correct maps while Parafac does. Additionally, we present and demonstrate a method to decrease the computational load of Parafac.

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