Archetypal Analysis for Modeling Multisubject fMRI Data

Abstract—Functional magnetic resonance imaging (fMRI) is widely used to measure brain function during various cognitive states. However, it remains a challenge to obtain low-rank models of functional networks in fMRI that have interpretable latent fea- tures and generalize across groups of subjects, due to significant in- tersubject variability in the signal structure and noise. Group-level modeling is typically performed using component decompositions such as independent component analysis (ICA), which represent data as a linear combination of latent brain patterns, or using clus- tering models, where data are assumed to be generated by a set of “prototype” time series. Archetypal analysis (AA) provides a promising alternative, combining the advantages of component- model flexibility with highly interpretable latent “archetypes” (similar to cluster-model prototypes). To date, AA has not been applied to group-level fMRI; a major limitation is that it does not generalize to multi-subject datasets, which may have significant variations in blood oxygenation-level-dependent signal and het- eroscedastic noise. We develop multi-subject AA (MS-AA), which accounts for group-level data by assuming that archetypal tempo- ral profiles have a common latent generator across subjects, ensur- ing that the temporal components are derived from a consistent set of brain regions. In addition, the model accounts for noise het- eroscedasticity by modeling subject- and voxel-specific noise vari- ance. This provides a novel approach to group-level modeling and an alternative to preexisting methods that account for inter-subject variability by extracting individual maps as a postprocessing step (e.g., dual-regression ICA), or assuming spatial dependency of maps across subjects (e.g., independent vector analysis). MS-AA shows robust performance when modelling archetypes for a mo- tor task experiment. The procedure extracts a “seed map” across subjects, used to provide brain parcellations with subject-specific temporal profiles. Our approach thus decomposes multisubject fMRI data into distinct interpretable component archetypes that may help to model both consistent group-level measures of fMRI data and individual variability.