Contributions a l’analyse de données multivoie : algorithmes et applications

Abstract : In this thesis we develop a framework for the extension of commonly used linear statistical methods (Fisher Discriminant Analysis, Logistical Regression, Cox regression and Regularized Canonical Correlation Analysis) to the multiway context. In contrast to their standard formulation, their multiway generalization relies on structural constraints imposed to the weight vectors that integrate the original tensor structure of the data within the optimization process. This structural constraint yields a more parsimonious and interpretable model. Different strategies to deal with high dimensionality are also considered. The application of these algorithms is illustrated on two real datasets: (i) serving for the discrimination of spectroscopy data for which all methods where tested and (ii) to predict the long term recovery of patients after traumatic brain injury from multi-modal brain Magnetic Resonance Imaging. In both datasets our methods yield valuable results compared to the standard approach.
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Olga Lechuga Lopez. Contributions a l’analyse de données multivoie : algorithmes et applications. Autre. Université Paris-Saclay, 2017. Français. ⟨NNT : 2017SACLC038⟩. ⟨tel-01619919⟩

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