Hierarchical nonlinear embedding reveals brain states and performance differences during working memory tasks

Investigation of the moment-to-moment changes in brain activity using functional magnetic resonance imaging (fMRI) is an emerging field. However, one of the major problems is how to represent and evaluate these temporal relationships from the high-dimensional fMRI data. While many linear approaches have been proposed, nonlinear dimensionality reduction approaches may offer better solutions for these high-dimensional data. In this work, we propose a hierarchical, dimensionality reduction framework for time-synchronized fMRI data based on diffusion maps—a type of nonlinear embedding—labeled 2step diffusion maps (2sDM). For evaluation, we apply the framework to task fMRI during a working memory task for two large, independent datasets. By applying the embedding on the time domain, we show that our framework can detect brain states as defined by task blocks. By applying the embedding on the subjects domain, we show that subjects can be separated by their working memory performance. Together, these results show the promise of 2sDM as a nonlinear embedding framework for fMRI data.