Nonlinear dimension reduction of fMRI data: the Laplacian embedding approach

In this paper, we introduce the use of nonlinear dimension reduction for the analysis of functional neuroimaging datasets. Using a Laplacian embedding approach, we show the power of this method to detect significant structures within the noisy and complex dynamics of fMRI datasets; it outperforms classical linear techniques in the discrimination of structures of interest. Moreover, it can also be used in a more constrained framework, allowing for an exploration of the manifold of the hemodynamic responses of interest. A solution is proposed for the issue of dimension selection, which is not yet completely satisfactory. However, our studies show the power of the method for data exploration, visualization and understanding.