Réunion

Geometry and time-series signal processing 

Annonce

Les demandes de prise en charge de mission sont à formuler avant le 19 octobre.

In many signal processing and time series applications (navigation, motion analysis, sensor networks, etc.), measured data evolve in structured, non-necessarily Euclidean spaces. Over the past few years, a new research trend has emerged, incorporating these geometric constraints (Lie groups, Riemannian manifolds, etc.) into data processing methods (change-point detection, filtering, etc.). In parallel, tools from algebraic geometry and topology (signature theory, topological data analysis) have shed new light on time series analysis. The purpose of this scientific workshop is to present the latest advances regarding the links between signal processing and geometry (in a broad sense).

The topics include (not limited)

• Signal processing on manifolds
• Change-point detection on non-Euclidean space
• Signature theory and rough path
• Topological data analysis (TDA)
• Statistical learning on geometric spaces
• Analysis of structured time series

Invited speakers

• Fréderic Chazal (INRIA Saclay) A Topological Approach for Anomaly Detection in Complex Time-Series Data The aim of this talk is to present a novel method based on Topological Data Analysis (TDA) for detecting structural anomalies in complex data sequences. We will focus on the problem of identifying changes in the global dependency structure between channels of multivariate time series, represented as a weighted dynamic graph. This work is a joint collaboration with Clément Levrard (University of Rennes) and Martin Royer (IRT SystemX).

• Marianne Clausel (CRAN/University of Lorraine)

• Karim Dahia (ONERA) Monte Carlo methods on Lie groups: application to Navigation. This presentation provides an overview of Monte Carlo methods for Bayesian state estimation, with a focus on extending them to systems that evolve on Lie groups. First, we introduce the probabilistic framework underlying Bayesian filtering, and discuss the challenges associated with nonlinear and non-Gaussian estimation problems. We then present the two main types of Monte Carlo approach: particle filtering and Sequential Markov chain Monte Carlo (MCMC) methods. The second part of the presentation focuses on state estimation when the state space is described by a Lie group. We discuss how particle filtering can be formulated directly on Lie groups, and how Sequential MCMC methods can be adapted to exploit this structure. These approaches provide flexible tools for representing and propagating complex probability distributions while respecting the geometry of the state space.Finally, we illustrate the proposed methods through navigation applications, in which position, velocity, orientation naturally lead to nonlinear estimation problems and, in many cases, to Lie group representations.

Call for contributions

Early-career researchers (Ph.D. students, postdocs, recently appointed assistant professors) are encouraged to apply. Please send your title and a short abstract (max. 1/2 page) to samy.labsir@ipsa.fr, laurent.oudre@ens-paris-saclay.fr , hugo.henneuse@univ-evry.fr,  by October 2.
Decisions on oral or poster presentations will be sent by October 9.

Organizers

• Samy Labsir (IPSA/TéSA–ISAE-SUPAERO)
• Laurent Oudre (Centre Borelli, ENS Paris-Saclay)
• Hugo Henneuse (Université Evry Paris-Saclay)