CLOT Denis

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We propose to illustrate in this thesis the significant contribution of functional data analysis to existing knowledge extraction techniques as well as to medical imaging, by applying functional principal component analysis (FPCA) to spatio-temporal deformation parameters of the canine left ventricle. Our work starts with a short review of the state of the art of KDD, which gives a synthetic view of the evolution of this research field at the interface of many disciplines. In a second part, we recall the principle of principal component analysis (PCA) and we detail its analysis protocol in order to establish a parallel facilitating the presentation of the generalization of PCA to the functional framework. Computational developments are proposed in order to allow the application of this method to large matrices, which will find its interest for our application. The CFPA is then presented in the mono and multifunctional frameworks. Some adjustments are proposed to overcome the limitations of the application protocol for the multifunctional case and a new analysis scheme is built to guide the interpretation of the results. Our proposal is first illustrated by the study of random variables with values in the set of continuous functions on a closed set of reals, which constitutes a simple framework. The generality of the model of the objects studied by the CFPA allows the enrichment of the data concerned by the methods of Data Mining. The fourth part presents an application revealing the potentiality of the CFPA for the study of complex data: the analysis of about thirty functional random variables, spatio-temporal parameters of deformation of the myocardium extracted from sequences of 3D images obtained by MRI of tissue marking. The method developed in this framework can be used by the cardiologist for the analysis of the cardiac dynamics in the healthy case or for the research of characterizations of the ischemic states of the myocardium. The concepts presented for the systematic exploratory analysis of 3D+T data can be applied to 2D+T data of a more common access in medical imaging. This work is part of a collaboration between CREATIS (UMR CNRS affiliated to INSERM UCBL1 INSA) and LASS (UMR CNRS UCBL1).