# Unveiling the higher-order organization of multivariate time series

arXiv: https://arxiv.org/abs/2203.10702 · HTML: https://mlsanity.com/paper/2203.10702/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Mar 2022.

## Built on by (most cited first, 17 of 17)

- [Learning High-Order Relationships of Brain Regions](https://mlsanity.com/paper/2312.02203/) (2023)
- [Dirac signal processing of higher-order topological signals](https://mlsanity.com/paper/2301.10137/) (2023)
- [Interaction Measures, Partition Lattices and Kernel Tests for High-Order Interactions](https://mlsanity.com/paper/2306.00904/) (2023)
- [Information-Theoretic Measures on Lattices for High-Order Interactions](https://mlsanity.com/paper/2408.07533/) (2024)
- [LAMPER: LanguAge Model and Prompt EngineeRing for zero-shot time series classification](https://mlsanity.com/paper/2403.15875/) (2024)
- [Dirac-Equation Signal Processing: Physics Boosts Topological Machine Learning](https://mlsanity.com/paper/2412.05132/) (2024)
- [Permutation-Free High-Order Interaction Tests](https://mlsanity.com/paper/2506.05963/) (2025)
- [Beyond Pairwise Connections: Extracting High-Order Functional Brain Network Structures under Global Constraints](https://mlsanity.com/paper/2510.09175/) (2025)
- [The Variance Brain Foundation Models Forgot: Third-Order Statistics Predict Cognition Where Billion-Parameter Models Fail](https://mlsanity.com/paper/2606.04010/) (2026)
- [HyperBrain: Anomaly Detection for Temporal Hypergraph Brain Networks](https://mlsanity.com/paper/2410.02087/) (2024)
- [Beyond holography: the entropic quantum gravity foundations of image processing](https://mlsanity.com/paper/2503.14048/) (2025)
- [PHEATPRUNER: Interpretable Data-centric Feature Selection for Multivariate Time Series Classification through Persistent Homology](https://mlsanity.com/paper/2504.18329/) (2025)
- [DCHO: A Decomposition-Composition Framework for Predicting Higher-Order Brain Connectivity to Enhance Diverse Downstream Applications](https://mlsanity.com/paper/2509.09696/) (2025)
- [Information-theoretic signatures of causality in Bayesian networks and hypergraphs](https://mlsanity.com/paper/2512.20552/) (2025)
- [Topological Signal Processing: An Application-Oriented Tutorial](https://mlsanity.com/paper/2605.22853/) (2026)
- [FLY-EVAL++: An Evidence-Driven Evaluation Protocol for Safety-Constrained Flight Prediction with Large Language Models](https://mlsanity.com/paper/2609.04021/) (2026)
- [T-SNN: Temporal Simplicial Neural Network for EEG Decoding](https://mlsanity.com/paper/2609.34002/) (2026)

## Abstract (arXiv)

Time series analysis has proven to be a powerful method to characterize several phenomena in biology, neuroscience and economics, and to understand some of their underlying dynamical features. Despite a plethora of methods have been proposed for the analysis of multivariate time series, most of them neglect the effect of non-pairwise interactions on the emerging dynamics. Here, we propose a novel framework to characterize the temporal evolution of higher-order dependencies within multivariate time series. Using network analysis and topology, we show that, unlike traditional tools based on pairwise statistics, our framework robustly differentiates various spatiotemporal regimes of coupled chaotic maps, including chaotic dynamical phases and various types of synchronization. Hence, using the higher-order co-fluctuation patterns in simulated dynamical processes as a guide, we highlight and quantify signatures of higher-order patterns in data from brain functional activity, financial markets, and epidemics. Overall, our approach sheds new light on the higher-order organization of multivariate time series, allowing a better characterization of dynamical group dependencies inherent to real-world data.