Manifold Learning for fMRI time-varying FC

Whole-brain functional connectivity (FC) measured with functional MRI (fMRI) evolve over time in meaningful ways at temporal scales going from years (e.g., development) to seconds (e.g., within-scan time-varyingFC(tvFC)). Yet, our ability to exploretvFCis severely constrained by its large dimensionality (several thousands). To overcome this difficulty, researchers seek to generate low dimensional representations (e.g.,2Dand3Dscatter plots) expected to retain its most informative aspects (e.g., relationships to behavior, disease progression). Limited prior empirical work suggests that manifold learning techniques (MLTs)—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 tvFCdata to lie on a low dimensional manifold. Second, we estimate what is the intrinsic dimension (i.e., minimum number of latent dimensions;ID) oftvFCdata manifolds. Third, we describe the inner workings of three state-of-the-artMLTs: Laplacian Eigenmaps (LE), T-distributed Stochastic Neighbor Embedding (T-SNE), and Uniform Manifold Approximation and Projection (UMAP). For each method, we empirically evaluate its ability to generate neuro-biologically meaningful representations oftvFCdata, as well as their robustness against hyper-parameter selection. Our results show thattvFCdata has anIDthat ranges between 4 and 26, and thatIDvaries significantly between rest and task states. We also show how all three methods can effectively capture subject identity and task being performed:UMAPandT-SNEcan capture these two levels of detail concurrently, but LEcould only capture one at a time. We observed substantial variability in embedding quality acrossMLTs, and within-MLTas 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 ofMLTstotvFCdata. Overall, we conclude that whileMLTscan be useful to generate summary views of labeledtvFCdata, their application to unlabeled data such as resting-state remains challenging.