A method for investigating the nonlinear dynamics of the human brain from analysis of functional MRI data

We have argued the importance of a differential geometric approach to describing the nonlinear features of massive data sets. Based on biological models, one would expect the behavior of the brain to be comparable with a nonlinear dynamical system. Preliminary results from an investigation of the nonlinearity of brain activation as measured by fMRI studies motivate a careful study as we have outlined. From identifying features of data (i.e. characterizations of linearity or nonlinearity) in the two-dimensional slices of massive data sets, it is possible to construct a Riemannian curvature tensor with which one can describe global behavior of points in a data set. We demonstrate results of feature extraction based on local principal component analysis and spline fitting on both synthetic and fMRI data