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Un point de vue sur des approches factorielles et probabilistes de la covariance. Application à l'analyse locale du mouvement

Abstract : This thesis deals with factorial and probabilistic approaches of the covariance, which can take an extraneous knowledge on the observations into account. Dealing with temporal data, the model we
adopt breaks the signal into a deterministic function depending on time and representing a trend and into a residual term. Factorial methods are devoted to studying the trend. We present a general formalism for the relational covariance as well as new properties that clarify the interpretation and the connexion with existing concepts. Relational covariance is embedded into various paradigms
such as principal component analysis (PCA), operator factor analysis and operator discriminant factor analysis. We show that relational PCA is a special case of Kernel PCA and Functional PCA and we illustrate that property through duality diagrams. The study of the residuals is carried out within the scope of probabilistic models based on covariance. At a first step, the residual term is assumed to be multi-Gaussian, hence we use a Wishart distribution for the empirical covariance, followed by a clustering procedure (EM algorithms). At a second step, we apply fractal analysis to the residual term that is modeled as a self similar process. The Hurst parameter is estimated for several sampling protocols and we study how the protocol specificity may influence this estimation. All these concepts are applied to movement analysis e.g. : motion capture of contemporary dance movements (factorial methods and clustering of Wishart mixture models), as well as marine biology (segmentation and fractal analysis).
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Submitted on : Wednesday, January 9, 2008 - 2:20:30 PM
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Sullivan Hidot. Un point de vue sur des approches factorielles et probabilistes de la covariance. Application à l'analyse locale du mouvement. Traitement du signal et de l'image [eess.SP]. Université de La Rochelle, 2007. Français. ⟨tel-00203241⟩

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