Euler Elastica Regularized Logistic Regression for Whole-Brain Decoding of fMRI Data

Objective: Multivariate pattern analysis methods have been widely applied to functional magnetic resonance imaging (fMRI) data to decode brain states. Due to the “high features, low samples” in fMRI data, machine learning methods have been widely regularized using various regularizations to avoid overfitting. Both total variation (TV) using the gradients of images and Euler's elastica (EE) using the gradient and the curvature of images are the two popular regulations with spatial structures. In contrast to TV, EE regulation is able to overcome the disadvantage of TV regulation that favored piecewise constant images over piecewise smooth images. In this study, we introduced EE to fMRI-based decoding for the first time and proposed the EE regularized multinomial logistic regression (EELR) algorithm for multi-class classification. Methods: We performed experimental tests on both simulated and real fMRI data to investigate the feasibility and robustness of EELR. The performance of EELR was compared with sparse logistic regression (SLR) and TV regularized LR (TVLR). Results: The results showed that EELR was more robustness to noises and showed significantly higher classification performance than TVLR and SLR. Moreover, the forward models and weights patterns revealed that EELR detected larger brain regions that were discriminative to each task and activated by each task than TVLR. Conclusion: The results suggest that EELR not only performs well in brain decoding but also reveals meaningful discriminative and activation patterns. Significance: This study demonstrated that EELR showed promising potential in brain decoding and discriminative/activation pattern detection.