Abstract：
In the brain, functional connections form a network whose topological organization can be described by graph-theoretic network diagnostics. These include characterizations of the community structure, such as modularity and participation coefficient, which have been shown to change over the course of childhood and adolescence. To investigate if such changes in the functional network are associated with changes in cognitive performance during development, network studies often rely on an arbitrary choice of preprocessing parameters, in particular the proportional threshold of network edges. Because the choice of parameter can impact the value of the network diagnostic, and therefore downstream conclusions, we propose to circumvent that choice by conceptualizing the network diagnostic as a function of the parameter. As opposed to a single value, a network diagnostic curve describes the connectome topology at multiple scales-from the sparsest group of the strongest edges to the entire edge set. To relate these curves to executive function and other covariates, we use scalar-on-function regression, which is more flexible than previous functional data-based models used in network neuroscience. We then consider how systematic differences between networks can manifest in misalignment of diagnostic curves, and consequently propose a supervised curve alignment method that incorporates auxiliary information from other variables. Our algorithm performs both functional regression and alignment via an iterative, penalized, and nonlinear likelihood optimization. The illustrated method has the potential to improve the interpretability and generalizability of neuroscience studies where the goal is to study heterogeneity among a mixture of function- and scalar-valued measures.
摘要：
在大脑中,功能连接形成一个网络，其拓扑组织可以通过图论网络诊断来描述。这些包括社区结构的特征，如模块化和参与系数，已被证明在童年和青春期的过程中会发生变化。为了研究功能网络的这种变化是否与发育过程中认知表现的变化有关，网络研究通常依赖于预处理参数的任意选择，特别是网络边缘的比例阈值。因为参数的选择会影响网络诊断的值，因此下游的结论，我们建议通过将网络诊断概念化为参数的函数来规避这种选择。与单一值相反，网络诊断曲线在多个尺度上描述了连接体拓扑结构-从最强边缘的最稀疏组到整个边缘集。为了将这些曲线与执行函数和其他协变量联系起来，我们使用标量函数回归，比以前在网络神经科学中使用的基于功能数据的模型更灵活。然后，我们考虑网络之间的系统差异如何表现为诊断曲线的错位，并因此提出了一种监督曲线对齐方法，该方法结合了其他变量的辅助信息。我们的算法通过迭代执行函数回归和对齐，受到惩罚,和非线性似然优化。所说明的方法有可能提高神经科学研究的可解释性和可泛化性，其目标是研究函数和标量值度量的混合之间的异质性。
