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Theses

Méthodes aléatoires pour l’apprentissage de données en grande dimension : application à l'apprentissage partagé

Abstract : This thesis deals with the study of random methods for learning large-scale data. Firstly, we propose an unsupervised approach consisting in the estimation of the principal components, when the sample size and the observation dimension tend towards infinity. This approach is based on random matrices and uses consistent estimators of eigenvalues and eigenvectors of the covariance matrix. Then, in the case of supervised learning, we propose an approach which consists in reducing the dimension by an approximation of the original data matrix and then realizing LDA in the reduced space. Dimension reduction is based on low–rank approximation matrices by the use of random matrices. A fast approximation algorithm of the SVD and a modified version as fast approximation by spectral gap are developed. Experiments are done with real images and text data. Compared to other methods, the proposed approaches provide an error rate that is often optimal, with a small computation time. Finally, our contribution in transfer learning consists in the use of the subspace alignment and the low-rank approximation of matrices by random projections. The proposed method is applied to data derived from benchmark database; it has the advantage of being efficient and adapted to large-scale data
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Nassara Elhadji Ille Gado. Méthodes aléatoires pour l’apprentissage de données en grande dimension : application à l'apprentissage partagé. Apprentissage [cs.LG]. Université de Technologie de Troyes, 2017. Français. ⟨NNT : 2017TROY0032⟩. ⟨tel-02965215⟩

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