用签名变换构建多变量时间序列集合的超图，提升分析鲁棒性。
Hypergraphs on high dimensional time series sets using signature transform
- 基于签名变换引入可控随机性构造超图
- 在合成数据上验证，对多序列集合有效
- 适合处理复杂时序数据的拓扑分析
近几十年来，超图及其通过拓扑数据分析（TDA）的分析已成为理解复杂数据结构的强大工具。已有多种方法用于在数据集上构建超图（在TDA框架中称为单纯复形），实现多个顶点之间的边连接。本文解决了从多变量时间序列集合构建超图的挑战。尽管先前工作聚焦于单个多元时间序列，本文将该框架扩展至处理此类序列集合。我们的方法通过利用签名变换的特性引入可控随机性，从而增强构建过程的鲁棒性。我们在合成数据集上验证了该方法，并取得了有前景的结果。
原文摘要 · Abstract (English)
In recent decades, hypergraphs and their analysis through Topological Data Analysis (TDA) have emerged as powerful tools for understanding complex data structures. Various methods have been developed to construct hypergraphs -- referred to as simplicial complexes in the TDA framework -- over datasets, enabling the formation of edges between more than two vertices. This paper addresses the challenge of constructing hypergraphs from collections of multivariate time series. While prior work has focused on the case of a single multivariate time series, we extend this framework to handle collections of such time series. Our approach generalizes the method proposed in Chretien and al. by leveraging the properties of signature transforms to introduce controlled randomness, thereby enhancing the robustness of the construction process. We validate our method on synthetic datasets and present promising results.
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