论文标题
使用拓扑数据分析建模和模拟网络中的依赖性
Modeling and Simulating Dependence in Networks Using Topological Data Analysis
论文作者
论文摘要
拓扑数据分析（TDA）方法在研究多元时间序列数据中的依赖模式方面变得越来越流行。特别是，大脑网络中的各种依赖模式可能与特定的任务和认知过程有关，这些任务和认知过程可以通过各种神经和认知障碍（例如阿尔茨海默氏症和帕金森氏症的疾病）以及注意力缺陷多动障碍（ADHD）来改变。由于在真实的大脑信号中没有具有已知依赖性模式的基础真相，因此在多元时间序列上测试新的TDA方法仍然是一个挑战。模拟对于评估提出的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，没有任何方法可以模拟具有特定和手动强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，以模拟其依赖性网络中具有特定数量的周期/孔的多元时间序列。此外，我们还提供了一种生成更高维拓扑特征的程序。
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.
