基于任务的fMRI精神分裂症实验数据的拓扑数据分析
Topological Data Analysis of Task-Based fMRI Data from Experiments on Schizophrenia
摘要：
我们使用计算代数拓扑学的方法来研究功能性脑网络，其中节点代表脑区域，加权边缘编码来自每个区域的fMRI时间序列的相似性。有了这些工具，它允许人们描述拓扑不变量，如高维数据中的循环，我们能够以一种补充基于成对相互作用的传统方法的方式来理解网络中的低维结构。在本文中，我们使用持续同源性分析网络，我们构建基于任务的功能磁共振成像数据从精神分裂症患者，健康对照组，精神分裂症患者的健康兄弟姐妹。因此，我们探索的持久性拓扑结构，如在这些网络中的不同尺度的循环。我们使用持久性景观和持久性图像创建输出摘要，从我们的持久性同源性计算，我们研究的持久性景观和图像使用$k$ -均值聚类和社区检测。基于我们对持久性景观的分析，我们发现兄弟队列的成员具有与其他两个队列不同的拓扑特征（特别是它们的一维循环）。从持久性图像中，我们能够区分所有三个受试者组，并确定环路中的大脑区域（具有四个或更多个边缘），使我们能够进行这些区分。
英文摘要：
We use methods from computational algebraic topology to study functional brain networks, in which nodes represent brain regions and weighted edges encode the similarity of fMRI time series from each region. With these tools, which allow one to characterize topological invariants such as loops in high-dimensional data, we are able to gain understanding into low-dimensional structures in networks in a way that complements traditional approaches that are based on pairwise interactions. In the present paper, we use persistent homology to analyze networks that we construct from task-based fMRI data from schizophrenia patients, healthy controls, and healthy siblings of schizophrenia patients. We thereby explore the persistence of topological structures such as loops at different scales in these networks. We use persistence landscapes and persistence images to create output summaries from our persistent-homology calculations, and we study the persistence landscapes and images using $k$-means clustering and community detection. Based on our analysis of persistence landscapes, we find that the members of the sibling cohort have topological features (specifically, their 1-dimensional loops) that are distinct from the other two cohorts. From the persistence images, we are able to distinguish all three subject groups and to determine the brain regions in the loops (with four or more edges) that allow us to make these distinctions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
