TL;DR. In this presentation, we will explore time series representations based on geometric approaches, focusing on methodologies that consider the temporal structure of data.
Abstract:
In many settings, ranging from behavioral neuroscience or industry to agricultural studies, complex systems (animals, machines, crops) are monitored for extended periods. The objective is to quantify the behavior of those complex systems using the collected time series in order to, e.g., discriminate between a control group and a test group, detect anomalies, or perform a longitudinal study.
Classical machine learning procedures struggle to consider the temporal structure of such signals. In this presentation, I will describe how a general methodology based on event detection (change point, motif, or anomaly) can help understand large time series data sets. I will focus on two geometric approaches that can provide intuitive and versatile representations.
Change point detection for non-Euclidean time series. Hadamard spaces, which encompass important data spaces like positive semidefinite matrices, certain Wasserstein spaces, and hyperbolic spaces, provide the right general framework to address the complexity of non-Euclidean time series. We propose a computationally efficient algorithm called HOP (Hadamard Optimal Partitioning) that detects changes in the sequence of so-called Fréchet means. The proposed method consistently estimates the change point locations. HOP is highly versatile, accommodating structural assumptions such as cyclic patterns and epidemic settings, making it unique in the literature.
Comparing time series using shape deformation analysis. We will describe an unsupervised representation learning (URL) algorithm for time series. The idea is to represent time series as deformations of a reference time series. The deformations are diffeomorphisms parameterized and learned by our method called TS-LDDMM. Once the deformations and the reference time series are learned, the vector representations of individual time series are given by the parametrization of their corresponding deformation. At the crossroads between URL for time series and shape analysis, the proposed algorithm handles irregularly sampled multivariate time series of variable lengths and provides shape-based representations of temporal data.
Articles:
Kostic, A., Runge, V., & Truong, C. (2025). Change Point Detection in Hadamard Spaces by Alternating Minimization. Proceedings of the International Conference on Artificial Intelligence and Statistics (AISTATS). Preprint: https://drive.google.com/file/d/1nn3xrcuLC-lNDYVe6Jah1qhP9bbKknuS/view
Germain, T., Gruffaz, S., Truong, C., Durmus, A. O., & Oudre, L. (2024). Shape analysis for time series. Advances in Neural Information Processing System (NeurIPS).