用功能性MRI(fMRI)测量的全脑功能连通性(FC)随着时间的推移在时间尺度上以有意义的方式演变(例如,开发)到秒[例如,扫描内时变FC(tvFC)]。然而,我们探索tvFC的能力受到其大维度(几千)的严重限制。为了克服这个困难,研究人员经常寻求生成低维表示(例如,2D和3D散点图)希望这些将保留数据的重要方面(例如,与行为和疾病进展的关系)。有限的先前经验工作表明,流形学习技术(MLT)-即那些寻求推断低维非线性表面的技术(即,流形)大多数数据所在的地方-是完成这项任务的好人选。在这里,我们详细探讨这种可能性。首先,我们讨论了为什么应该期望tvFC数据位于低维流形上。第二,我们估计什么是内在维度(ID;即,tvFC数据流形的最小潜在维数)。第三,我们描述了三种最先进的MLT的内部工作原理:拉普拉斯特征映射(LE),T分布随机邻居嵌入(T-SNE),和统一流形逼近和投影(UMAP)。对于每种方法,我们根据经验评估其生成tvFC数据的神经生物学有意义表示的能力,以及它们对超参数选择的鲁棒性。我们的结果表明,tvFC数据的ID范围在4到26之间,并且该ID在休息和任务状态之间显着变化。我们还展示了所有三种方法如何有效地捕获正在执行的主题身份和任务:UMAP和T-SNE可以同时捕获这两个级别的细节,但是LE一次只能捕获一个。我们观察到MLT的嵌入质量有很大差异,和MLT内作为超参数选择的函数。为了缓解这个问题,我们提供了可以为未来研究提供信息的启发式方法。最后,我们还证明了在合并跨受试者的数据时特征归一化的重要性,以及时间自相关在将MLT应用于tvFC数据中所起的作用.总的来说,我们得出的结论是,虽然MLT可以用于生成带标签的tvFC数据的摘要视图,它们对未标记数据(如静息状态)的应用仍然具有挑战性。
Whole-brain functional connectivity (FC) 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 FC (tvFC)]. Yet, our ability to explore tvFC is severely constrained by its large dimensionality (several thousands). To overcome this difficulty, researchers often seek to generate low dimensional representations (e.g., 2D and 3D 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 (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 tvFC data to lie on a low dimensional manifold. Second, we estimate what is the intrinsic dimension (ID; i.e., minimum number of latent dimensions) of tvFC data manifolds. Third, we describe the inner workings of three state-of-the-art MLTs: Laplacian Eigenmaps (LEs), 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 of tvFC data, as well as their robustness against hyper-parameter selection. Our results show that tvFC data has an ID that ranges between 4 and 26, and that ID varies significantly between rest and task states. We also show how all three methods can effectively capture subject identity and task being performed: UMAP and T-SNE can capture these two levels of detail concurrently, but LE could only capture one at a time. We observed substantial variability in embedding quality across MLTs, and within-MLT 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 MLTs to tvFC data. Overall, we conclude that while MLTs can be useful to generate summary views of labeled tvFC data, their application to unlabeled data such as resting-state remains challenging.