利用拓扑数据分析建模和模拟网络中的依赖关系
Modeling and Simulating Dependence in Networks Using Topological Data Analysis
AI总结：
本文提出了一种新的方法，用于模拟具有特定连接模式的多元时间序列数据，并生成更高维拓扑特征，以评估TDA方法在分析网络依赖关系中的性能。
摘要：
拓扑数据分析（TDA）方法正日益受到关注，用于研究多元时间序列数据中的依赖模式。特别是，大脑网络中的各种依赖模式可能与特定任务和认知过程相关，这些模式可能受到阿尔茨海默病、帕金森病以及注意缺陷多动障碍（ADHD）等神经和认知损伤的影响。由于真实脑信号中没有已知的依赖模式的地面真相，对新TDA方法进行多元时间序列测试仍是一个挑战。模拟对于评估所提出TDA方法和测试程序的性能以及创建基于计算的置信区间至关重要。据我们所知，目前尚无方法能够模拟具有特定和手动施加的连接模式的多元时间序列数据。在本文中，我们提出了一种新的方法，用于模拟具有特定循环/孔数的依赖网络的多元时间序列。此外，我们还提供了一种生成更高维拓扑特征的程序。
英文摘要：
Topological data analysis (TDA) approaches are becoming increasingly popular for studying the dependence patterns in multivariate time series data. In particular, various dependence patterns in brain networks may be linked to specific tasks and cognitive processes, which can be altered by various neurological and cognitive impairments such as Alzheimer's and Parkinson's diseases, as well as attention deficit hyperactivity disorder (ADHD). Because there is no ground-truth with known dependence patterns in real brain signals, testing new TDA methods on multivariate time series is still a challenge. Simulations are crucial for evaluating the performance of proposed TDA methods and testing procedures as well as for creating computation-based confidence intervals. To our knowledge, there are no methods that simulate multivariate time series data with specific and manually imposed connectivity patterns. In this paper we present a novel approach to simulate multivariate time series with specific number of cycles/holes in its dependence network. Furthermore, we also provide a procedure for generating higher dimensional topological features.
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