Abstract — In many biomedical studies, data take the form of multivariate time series, whose dimensions are highly correlated. In order to take this structure into account in data processing, graphs appear as a valid solution, defining a new analysis domain that can be considered as a generalization of the 1D or 2D grid used in signal or image processing. In recent years, Graph Signal Processing (GSP) has emerged as a new research area aiming at extending signal processing tools (filtering, Fourier analysis, etc…) to signals defined on irregular domains. This talk will review the main tools of GSP and will propose two new contributions. First, a graph learning algorithm that learns a graph structure from a multivariate time series. Second, an interpolation method for multivariate time series that uses the graph structure to improve reconstruction.
– P. Humbert, B. Le Bars, L. Oudre, A. Kalogeratos, and N. Vayatis. Learning Laplacian Matrix from Graph Signals with Sparse Spectral Representation. Journal of Machine Learning Research, 22(195):1-47, 2021
– A. Mazarguil, L. Oudre, and N. Vayatis. Non-smooth interpolation of graph signals. Signal Processing, 196:108480, 2022.
Bio — Laurent Oudre is currently a Full Professor at Centre Borelli of the Ecole Normale Supérieure Paris-Saclay. He leads a team of about ten young researchers and has been working for about fifteen years on signal processing, pattern recognition and machine learning for time series. His work covers a wide range of issues (event detection, feature extraction, unsupervised or semi-supervised approaches, representation learning and graph signal processing). His scientific projects are mainly focused on AI applications in health and industry, often with a strong interdisciplinary component. He is also involved in initiatives around reproducible research and acculturation to AI (especially for the medical community). He is the author of more than fifty patents and articles in international peer-reviewed journals and conferences.