论文标题
时间序列分类的持续同源方法
A Persistent Homology Approach to Time Series Classification
论文作者
论文摘要
拓扑数据分析（TDA）是计算拓扑的不断上升领域，其中数据集的拓扑结构可以通过持续的同源性观察到。通过考虑一系列级别的集合，人们获得了跟踪拓扑信息变化的过滤。这些更改可以记录在称为{\ it持续图}的多组中。将存储在持久性图中的信息转换为与现代机器学习算法兼容的形式是TDA研究的主要研究。 {\ It持久性曲线}是一种最近开发的框架，提供了一种规范和灵活的方式，可以将持久图中显示的信息编码为向量。在这项工作中，我们根据持久性曲线提出了一组新的指标。我们证明了拟议的指标的稳定性。最后，我们将这些指标应用于UCR时间序列分类存档。这些经验结果表明，在大多数情况下，我们的指标的性能优于相关基准，并需要进一步研究。
Topological Data Analysis (TDA) is a rising field of computational topology in which the topological structure of a data set can be observed by persistent homology. By considering a sequence of sublevel sets, one obtains a filtration that tracks changes in topological information. These changes can be recorded in multi-sets known as {\it persistence diagrams}. Converting information stored in persistence diagrams into a form compatible with modern machine learning algorithms is a major vein of research in TDA. {\it Persistence curves}, a recently developed framework, provides a canonical and flexible way to encode the information presented in persistence diagrams into vectors. In this work, we propose a new set of metrics based on persistence curves. We prove the stability of the proposed metrics. Finally, we apply these metrics to the UCR Time Series Classification Archive. These empirical results show that our metrics perform better than the relevant benchmark in most cases and warrant further study.
