Global ETD Search

1	Discrimination robuste par méthode à noyaux / Robust discrimination using kernel approach Lachaud, Antoine 17 December 2015 (has links) La thèse porte sur l'intégration d éléments explicatifs au sein d'un modèle de classification. Plus précisément la solution proposée se compose de la combinaison entre un algorithme de chemin de régularisation appelé DRSVM et une approche noyau appelée KERNEL BASIS. La première partie de la thèse consiste en l'amélioration d'un algorithme appelé DRSVM à partir d'une reformulation du chemin via la théorie de la sous-différentielle. La seconde partie décrit l'extension de l'algorithme DRSVM au cadre KERNEL BASIS via une approche dictionnaire. Enfin une série d'expérimentation sont réalisées afin de valider l'aspect interprétable du modèle. / This thesis aims at finding classification rnodeIs which include explanatory elements. More specifically the proposed solution consists in merging a regularization path algorithm called DRSVM with a kernel approach called KERNEL BASIS. The first part of the thesis focuses on improving an algorithm called DRSVM from a reformulation of the thanks to the suh-differential theory. The second part of the thesis describes the extension of DRSVM afgorithm under a KERNEL BASIS framework via a dictionary approach. Finally, a series of experiments are conducted in order to validate the interpretable aspect of the rnodel. Méthode à noyaux Théorie sous-différentielle Discrimination robuste DRSVM Kernel Basis Support vector machines
2	Fast Order Basis and Kernel Basis Computation and Related Problems Zhou, Wei 28 November 2012 (has links) In this thesis, we present efficient deterministic algorithms for polynomial matrix computation problems, including the computation of order basis, minimal kernel basis, matrix inverse, column basis, unimodular completion, determinant, Hermite normal form, rank and rank profile for matrices of univariate polynomials over a field. The algorithm for kernel basis computation also immediately provides an efficient deterministic algorithm for solving linear systems. The algorithm for column basis also gives efficient deterministic algorithms for computing matrix GCDs, column reduced forms, and Popov normal forms for matrices of any dimension and any rank. We reduce all these problems to polynomial matrix multiplications. The computational costs of our algorithms are then similar to the costs of multiplying matrices, whose dimensions match the input matrix dimensions in the original problems, and whose degrees equal the average column degrees of the original input matrices in most cases. The use of the average column degrees instead of the commonly used matrix degrees, or equivalently the maximum column degrees, makes our computational costs more precise and tighter. In addition, the shifted minimal bases computed by our algorithms are more general than the standard minimal bases. polynomial matrix computation algorithm complexity computer algebra order basis kernel basis linear system solving matrix inverse determinant unimodular completion Popov form Hermite form column reduced form GCD matrix GCD rank rank profile column basis Computer Science
3	Fast Order Basis and Kernel Basis Computation and Related Problems Zhou, Wei 28 November 2012 (has links) In this thesis, we present efficient deterministic algorithms for polynomial matrix computation problems, including the computation of order basis, minimal kernel basis, matrix inverse, column basis, unimodular completion, determinant, Hermite normal form, rank and rank profile for matrices of univariate polynomials over a field. The algorithm for kernel basis computation also immediately provides an efficient deterministic algorithm for solving linear systems. The algorithm for column basis also gives efficient deterministic algorithms for computing matrix GCDs, column reduced forms, and Popov normal forms for matrices of any dimension and any rank. We reduce all these problems to polynomial matrix multiplications. The computational costs of our algorithms are then similar to the costs of multiplying matrices, whose dimensions match the input matrix dimensions in the original problems, and whose degrees equal the average column degrees of the original input matrices in most cases. The use of the average column degrees instead of the commonly used matrix degrees, or equivalently the maximum column degrees, makes our computational costs more precise and tighter. In addition, the shifted minimal bases computed by our algorithms are more general than the standard minimal bases. polynomial matrix computation algorithm complexity computer algebra order basis kernel basis linear system solving matrix inverse determinant unimodular completion Popov form Hermite form column reduced form GCD matrix GCD rank rank profile column basis Computer Science

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