A Lanczos-view on Independent Component Analysis of fMRI Data
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Analysis of resting-state fMRI data is commonly done by a combination of the two signal processing methods Principal Component Analysis (PCA) and Independent Component analysis (ICA). In this thesis, a possible error caused by the combination of the two methods are pointed out. The error is described theoretically and by several examples. Furthermore a new, alternative algorithm is introduced. The new algorithm is performing the ICA by a Lanczos method on a four dimensional tensor without a PCA preprocessing step and may thereby overcome some of the possible errors. This Lanczos-based method is suited to deal with large datasets where only a limited number of components are interesting. The convergence of the method, and thereby the ordering of the independent components, are heavily dependent of the spectral properties of the data. Without prior knowledge of the eigenvalues, the Lanczos-based method may give unsatisfactory results. Nevertheless, the framework in which the Lanczos-ICA method is based, proves to be a powerful base for future ICA methods and fMRI analysis algorithms.