Multivariate analysis with tensors and graphs – application to neuroscience.

Summary How to extract information from multivariate data has become a fundamental question in recent years. Indeed, their increasing availability has highlighted the limitations of standard models and the need to evolve towards more versatile methods. The main objective of this thesis is to provide methods and algorithms taking into account the structure of multivariate signals. Well-known examples of such signals are images, stereo audio signals, and multi-channel electroencephalography signals. Among existing approaches, we specifically focus on those based on graph or tensor induced structure which have already attracted increasing attention due to their ability to better exploit the multivariate aspect of the data and their underlying structure. Although this thesis takes the study of general anesthesia as its preferred application context, the methods developed are suitable for a wide spectrum of multivariate structured data.