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.

L0-regularized time-varying sparse inverse covariance estimation for tracking dynamic fMRI brain networks.

Exploration of time-varying functional brain connectivity based on functional Magnetic Resonance Imaging (fMRI) data is important for understanding dynamic brain mechanisms. l1-penalized inverse covariance is a common measure for the inference of sparse structure of functional brain networks, and it has been recently extended to estimate time-varying sparse brain networks by using a sliding window and incorporating a smoothing constraint on temporal variation. However, l1 penalty cannot induce maximum sparsity, as compared with l0 penalty, so l0 penalty is supposed to have superior quality on inverse covariance estimation. This paper introduces a novel time-varying sparse inverse covariance estimation method based on dual l0-penalties (DLP). The new DLP method estimates the sparse inverse covariance by minimizing an l0-penalized log-likelihood function and an extra l0 penalty on temporal homogeneity. A cyclic descent optimization algorithm is further developed to localize the minimum of the objective function. Experiment results on simulated signals show that the proposed DLP method can achieve better performance than conventional l1-penalized methods in estimating time-varying sparse network structures under different scenarios.