Dynamical components analysis of fMRI data through kernel PCA

In parallel with standard model-based methods for the analysis of fMRI data, exploratory methods--such as PCA, ICA, and clustering--have been developed to give an account of the dataset with minimal priors: no assumption is made on the data content itself, but the data structure is assumed to show some properties (decorrelation, independence) that allow for the detection of structures of interest. In this paper, we present an alternative that tries to take into account some relevant knowledge for the analysis of the dataset, e.g., the experimental paradigm, while keeping the flexibility of exploratory methods: we use a prior temporal modeling of the data that characterizes each voxel time course. Two implementations are proposed: one based on the General Linear Model, the other one on more flexible short-term predictors, whose complexity is controlled by a Minimum Description Length approach. However, our main concern here is the construction of a multivariate model; the latter is performed with the help of a kernel PCA method that builds a redundant representation of the data through the nonlinearity of the kernel. This allows for a refinement in the description of the (temporal) patterns of interest. In particular, this helps in the characterization of subtle variations in the response to different experimental conditions. We illustrate the usefulness of nonlinearity through the analysis of a synthetic dataset and show on a real dataset how it helps to interpret the experimental results.