LEICA: Laplacian eigenmaps for group ICA decomposition of fMRI data.

Independent component analysis (ICA) is a data-driven method that has been increasingly used for analyzing functional Magnetic Resonance Imaging (fMRI) data. However, generalizing ICA to multi-subject studies is non-trivial due to the high-dimensionality of the data, the complexity of the underlying neuronal processes, the presence of various noise sources, and inter-subject variability. Current group ICA based approaches typically use several forms of the Principal Component Analysis (PCA) method to extend ICA for generating group inferences. However, linear dimensionality reduction techniques have serious limitations including the fact that the underlying BOLD signal is a complex function of several nonlinear processes. In this paper, we propose an effective non-linear ICA-based model for extracting group-level spatial maps from multi-subject fMRI datasets. We use a non-linear dimensionality reduction algorithm based on Laplacian eigenmaps to identify a manifold subspace common to the group, such that this mapping preserves the correlation among voxels' time series as much as possible. These eigenmaps are modeled as linear mixtures of a set of group-level spatial features, which are then extracted using ICA. The resulting algorithm is called LEICA (Laplacian Eigenmaps for group ICA decomposition). We introduce a number of methods to evaluate LEICA using 100-subject resting state and 100-subject working memory task fMRI datasets from the Human Connectome Project (HCP). The test results show that the extracted spatial maps from LEICA are meaningful functional networks similar to those produced by some of the best known methods. Importantly, relative to state-of-the-art methods, our algorithm compares favorably in terms of the functional cohesiveness of the spatial maps generated, as well as in terms of the reproducibility of the results.