Nonlinear Dimension Reduction and Activation Detection for fMRI Dataset

Functional magnetic resonance imaging (fMRI) has been established as a powerful method for brain mapping. Different physical phenomena contribute to the dynamical changes in the fMRI signal, the task-related hemodynamic responses, non-task-related physiological rhythms, machine and motion artifacts, etc. In this paper, we propose a new approach for fMRI data analysis. Each fMRI time series is viewed as a point in RT . We are interested in learning the organization of the points in high dimensions and extracting useful information for data classification. A nonlinear manifold learning technique is applied to obtain a low dimensional embedding of a dataset. The embedding differentiates time series with different temporal patterns. By assuming that the subset of activated time series forms a low dimensional structure, we partition the dataset and separate subsets of points with low dimensionality. The correspondence between low dimensional subsets and time series that contain task-related responses is verified and the activation maps are generated accordingly. The proposed approach is data-driven. It does not require a model for the hemodynamic response. We have conducted several experiments with synthetic and in-vivo datasets that demonstrate the performance of our approach.