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Développement de méthodes d'analyse de données en ligne

Romain Bar 1, 2
1 BIGS - Biology, genetics and statistics
Inria Nancy - Grand Est, IECL - Institut Élie Cartan de Lorraine
Abstract : High dimensional data are supposed to be independent on-line observations of a random vector. In the second chapter, the latter is denoted by Z and sliced into two random vectors R et S and data are supposed to be identically distributed. A recursive method of sequential estimation of the factors of the projected PCA of R with respect to S is defined. Next, some particular cases are investigated : canonical correlation analysis, canonical discriminant analysis and canonical correspondence analysis ; in each case, several specific methods for the estimation of the factors are proposed. In the third chapter, data are observations of the random vector Zn whose expectation θn varies with time. Let Zn_tilde = Zn − θn and suppose that the vectors Zn_tilde form an independent and identically distributed sample of a random vector Z_tilde. Stochastic approximation processes are used to estimate on-line direction vectors of the principal axes of a partial principal components analysis (PCA) of Z_tilde. This is applied next to the particular case of a partial generalized canonical correlation analysis (gCCA) after defining a stochastic approximation process of the Robbins-Monro type to estimate recursively the inverse of a covariance matrix. In the fourth chapter, the case when both expectation and covariance matrix of Zn vary with time n is considered. Finally, simulation results are given in chapter 5.
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Romain Bar. Développement de méthodes d'analyse de données en ligne. Statistiques [math.ST]. Université de Lorraine, 2013. Français. ⟨NNT : 2013LORR0216⟩. ⟨tel-01750512v2⟩

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