Hypergraphs on high dimensional time series sets using signature transform

2025-07-21

AI Summary

Existing hypergraph construction methods are limited to single multivariate time series (MTS) and fail to capture high-order inter-series dependencies. Method: This paper proposes the first stochastic hypergraph construction framework for collections of MTS. Its core innovation is the novel integration of the signature transform into hypergraph modeling—leveraging its hierarchical feature extraction and controllable stochasticity, jointly with topological data analysis (TDA), to enable semantic-aware, high-order relational modeling across high-dimensional time series. Contribution/Results: The method generalizes conventional hypergraph approaches to multi-series settings, significantly enhancing structural robustness and representational capacity. Experiments on synthetic datasets demonstrate that the resulting hypergraphs exhibit stable, interpretable semantic structures, establishing a new paradigm for analyzing complex temporal associations.

Technology Category

• Machine Learning: Time-Series/Data Streams
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Data Mining & Knowledge Management: Mining of Spatial, Temporal or Spatio-Temporal Data

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Web Mining and Content Analysis: Bridging structured and unstructured data

Abstract

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.

Problem

• Construct hypergraphs from multivariate time series collections
• Extend framework to handle multiple time series datasets
• Enhance robustness using signature transforms and randomness

Innovation

• Hypergraphs on high dimensional time series
• Signature transforms introduce controlled randomness
• Extends framework to multiple time series