A related paper has been accepted for publication in NeuroImage )

We discuss model-free analysis of multi-subject or multi-session FMRI data by extending the single-session Probabilistic Independent Component Analysis model (PICA; [2]) to higher dimensions. This results in a threeway decomposition which represents the different signals and artefacts present in the data, in terms of their temporal, spatial and subject-dependent variations. The technique is derived from and compared with Parallel Factor Analysis (PARAFAC; [11]). Using simulated data as well as data from multi-session and multi-subject FMRI studies we demonstrate that the tensor-PICA approach is able to efficiently and accurately extract signals of interest in the spatial, temporal and subject/session domain. The final decompositions improve upon PARAFAC results in terms of greater accuracy, reduced interference between the different estimated sources (reduced cross-talk), robustness (against deviations of the data from modelling assumptions and against overfitting) and computational speed. On real FMRI ’activation’ data, the tensor-PICA approach is able to extract plausible activation maps, time courses and session/subject modes as well as provide a rich description of additional processes of interest such as image artefacts or secondary activation patterns. The resulting data decomposition gives simple and useful representations of multi-subject/multi-session FMRI data that can aid the interpretation and optimisation of group FMRI studies beyond what can be achieved using model-based analysis techniques.