Manifold learning for fMRI time-varying functional connectivity.

Whole-brain functional connectivity () measured with functional MRI (fMRI) evolves over time in meaningful ways at temporal scales going from years (e.g., development) to seconds [e.g., within-scan time-varying ()]. Yet, our ability to explore is severely constrained by its large dimensionality (several thousands). To overcome this difficulty, researchers often seek to generate low dimensional representations (e.g., and scatter plots) hoping those will retain important aspects of the data (e.g., relationships to behavior and disease progression). Limited prior empirical work suggests that manifold learning techniques ()-namely those seeking to infer a low dimensional non-linear surface (i.e., the manifold) where most of the data lies-are good candidates for accomplishing this task. Here we explore this possibility in detail. First, we discuss why one should expect tv data to lie on a low dimensional manifold. Second, we estimate what is the intrinsic dimension (; i.e., minimum number of latent dimensions) of data manifolds. Third, we describe the inner workings of three state-of-the-art : Laplacian Eigenmaps (), T-distributed Stochastic Neighbor Embedding (), and Uniform Manifold Approximation and Projection (). For each method, we empirically evaluate its ability to generate neuro-biologically meaningful representations of data, as well as their robustness against hyper-parameter selection. Our results show that data has an that ranges between 4 and 26, and that varies significantly between rest and task states. We also show how all three methods can effectively capture subject identity and task being performed: and can capture these two levels of detail concurrently, but could only capture one at a time. We observed substantial variability in embedding quality across , and within- as a function of hyper-parameter selection. To help alleviate this issue, we provide heuristics that can inform future studies. Finally, we also demonstrate the importance of feature normalization when combining data across subjects and the role that temporal autocorrelation plays in the application of to data. Overall, we conclude that while can be useful to generate summary views of labeled data, their application to unlabeled data such as resting-state remains challenging.