Supervised nonlinear dimension reduction of functional magnetic resonance imaging data using Sliced Inverse Regression

Dimension reduction is essential for identifying a small set of discriminative features that are predictive of behavior or cognition from high-dimensional functional magnetic resonance imaging (fMRI) data. However, conventional linear dimension reduction techniques cannot reduce the dimension effectively if the relationship between imaging data and behavioral parameters are nonlinear. In the paper, we proposed a novel supervised dimension reduction technique, named PC-SIR (Principal Component - Sliced Inverse Regression), for analyzing high-dimensional fMRI data. The PC-SIR method is an important extension of the renowned SIR method, which can achieve the effective dimension reduction (e.d.r.) directions even the relationship between class labels and predictors is nonlinear but is unable to handle high-dimensional data. By using PCA prior to SIR to orthogonalize and reduce the predictors, PC-SIR can overcome the limitation of SIR and thus can be used for fMRI data. Simulation showed that PC-SIR can result in a more accurate identification of brain activation as well as better prediction than support vector regression (SVR) and partial least square regression (PLSR). Then, we applied PC-SIR on real fMRI data recorded in a pain stimulation experiment to identify pain-related brain regions and predict the pain perception. Results on 32 subjects showed that PC-SIR can lead to significantly higher prediction accuracy than SVR and PLSR. Therefore, PC-SIR could be a promising dimension reduction technique for multivariate pattern analysis of fMRI.