Persistent homology (PH) characterizes the shape of brain networks through the persistence features. Group comparison of persistence features from brain networks can be challenging as they are inherently heterogeneous. A recent scale-space representation of persistence diagram (PD) through heat diffusion reparameterizes using the finite number of Fourier coefficients with respect to the Laplace-Beltrami (LB) eigenfunction expansion of the domain, which provides a powerful vectorized algebraic representation for group comparisons of PDs. In this study, we advance a transposition-based permutation test for comparing multiple groups of PDs through the heat-diffusion estimates of the PDs. We evaluate the empirical performance of the spectral transposition test in capturing within- and between-group similarity and dissimilarity with respect to statistical variation of topological noise and hole location. We also illustrate how the method extends naturally into a clustering scheme by subtyping individuals with post-stroke aphasia through the PDs of their resting-state functional brain networks.

翻译：持续同调（PH）通过持续特征刻画脑网络的形状。由于脑网络持续特征本质上是异质的，对其进行组间比较颇具挑战。近期一种通过热扩散对持续图（PD）进行尺度空间表示的方法，利用域上拉普拉斯-贝尔特拉米（LB）本征函数展开的有限个傅里叶系数进行重参数化，为持续图的组间比较提供了强大的向量化代数表示。本研究提出一种基于转置的置换检验，通过持续图的热扩散估计对多组持续图进行比较。我们评估了谱转置检验在捕捉组内与组间相似性和差异性方面的实证表现，同时考虑了拓扑噪声和空洞位置统计变异的影响。此外，我们还展示了该方法如何自然扩展为聚类方案——通过静息态功能脑网络的持续图对脑卒中后失语症个体进行亚型分类。