Gaussian process based independent analysis for temporal source separation in fMRI.

Functional Magnetic Resonance Imaging (fMRI) gives us a unique insight into the processes of the brain, and opens up for analyzing the functional activation patterns of the underlying sources. Task-inferred supervised learning with restrictive assumptions in the regression set-up, restricts the exploratory nature of the analysis. Fully unsupervised independent component analysis (ICA) algorithms, on the other hand, can struggle to detect clear classifiable components on single-subject data. We attribute this shortcoming to inadequate modeling of the fMRI source signals by failing to incorporate its temporal nature. fMRI source signals, biological stimuli and non-stimuli-related artifacts are all smooth over a time-scale compatible with the sampling time (TR). We therefore propose Gaussian process ICA (GPICA), which facilitates temporal dependency by the use of Gaussian process source priors. On two fMRI data sets with different sampling frequency, we show that the GPICA-inferred temporal components and associated spatial maps allow for a more definite interpretation than standard temporal ICA methods. The temporal structures of the sources are controlled by the covariance of the Gaussian process, specified by a kernel function with an interpretable and controllable temporal length scale parameter. We propose a hierarchical model specification, considering both instantaneous and convolutive mixing, and we infer source spatial maps, temporal patterns and temporal length scale parameters by Markov Chain Monte Carlo. A companion implementation made as a plug-in for SPM can be downloaded from https://github.com/dittehald/GPICA.

Evaluating Model Misspecification in Independent Component Analysis.

Independent component analysis (ICA) is a popular blind source separation technique used in many scientific disciplines. Current ICA approaches have focused on developing efficient algorithms under specific ICA models, such as instantaneous or convolutive mixing conditions, intrinsically assuming temporal independence or autocorrelation of the sources. In practice, the true model is not known and different ICA algorithms can produce very different results. Although it is critical to choose an ICA model, there has not been enough research done on evaluating mixing models and assumptions, and how the associated algorithms may perform under different scenarios. In this paper, we investigate the performance of multiple ICA algorithms under various mixing conditions. We also propose a convolutive ICA algorithm for echoic mixing cases. Our simulation studies show that the performance of ICA algorithms is highly dependent on mixing conditions and temporal independence of the sources. Most instantaneous ICA algorithms fail to separate autocorrelated sources, while convolutive ICA algorithms depend highly on the model specification and approximation accuracy of unmixing filters.