TopTime: Topological and statistical methods for time series data (2024-2026)
INRIA Associated Team between DataShape and Australian National University (ANU).
Team members
On the INRIA side:
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Nina Otter, (PI), ISFP, DataShape group (INRIA-Saclay)
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Frédéric Chazal, Directeur de recherche, DataShape group (INRIA-Saclay)
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Marc Glisse, chargé de Recherche, DataShape group (INRIA-Saclay)
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Mathieu Carrière, chargé de Recherche, DataShape group (INRIA-Saclay)
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Charles Arnal, postdoc, DataShape group (Inria-Saclay)
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Hannah Schreiber, software engineer, DataShape group (INRIA Université Côte d’Azur)
On the ANU side:
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Katharine Turner (co-PI), Senior Lecturer, Mathematical Sciences Institute, ANU
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Vanessa Robins, Associate Professor, School of Physics, ANU
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James Nichols, Lecturer, Biological Data Science Institute, ANU
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Musashi Koyama, PhD Student, School of Physics, ANU
Motivations and scientific objectives
Methods from the field of Topological Data Analysis have been applied successfully to data from a variety of domains. At the same time, there has been less work done on studying in a principled way how such methods can be used to study data that changes dynamically over time. In this project we will develop TDA methods to study what we call generalised time series, namely continuously varying families of spaces. Examples include classical time series, dynamic point clouds, and dynamic networks. We will develop both our theoretical understanding of the topology of generalised time series, as well as develop efficient algorithms, and apply the methods to dynamic data arising from climate science, biology and finance.
We believe that there is a real need to develop topological and statistical methods to study generalised time series, both to put existing experimental findings on a more principled footing, as well as to gain new insights into this type of data. We are also convinced that these challenges need to be addressed both from a mathematical side as well as from the algorithmic/application side. Our main objectives for the three years will thus follow two axes: we will develop theoretical foundations to study generalised time series, and we will address specific problems arising in different application domains, while developing state-of-the-art software packages of these methods, making our tools accessible and easy to use to a broad audience of data scientists.
1. Topological and statistical methods for time series.
Our objective is to develop methods that allow to use persistent homology to study classical and generalised time series data. We intend in particular to develop topologically-inspired data imputation methods, robust descriptors of topological features for time series, as well as to study topological properties of random time series. Our ultimate objective is to initiate a principled study of the topology and geometry of dynamic data.
2. Efficient software implementations and applications.
We will tackle specific problems arising in different application domains, and develop efficient software implementations of the methods. The DataShape team has developed and maintains Gudhi, one of the main libraries for topological data analysis. We will integrate the implementations of the new methods into this library. We will study time series arising from climate data in the first year, and biology (e.g., dynamical networks, important for the modelling of contagions), and financial data in the last two years.
