Combinaison sans répétition | EPFL Graph Search

Les combinaisons sont un concept de mathématiques, plus précisément de combinatoire, décrivant les différentes façons de choisir un nombre donné d'objets dans un ensemble de taille donnée, lorsque les objets sont discernables et que l'on ne se soucie pas de l'ordre dans lequel les objets sont placés ou énumérés. Le nom complet, bien que peu usité est combinaison sans répétition de n éléments pris k à k. Autrement dit, les combinaisons de taille k d'un ensemble E de cardinal n sont les sous-ensembles de E qui ont pour taille k. Contrairement aux arrangements, les combinaisons s'intéressent uniquement aux éléments choisis parmi l'ensemble, et non à l'ordre dans lequel ils sont tirés. Un exemple est la main obtenue en tirant simultanément k cartes dans un jeu de n cartes. De même, au jeu du loto, le tirage de 6 numéros parmi 49 ne fait pas référence à l'ordre de tirage des boules, mais au tirage final vu comme un ensemble non ordonné de 6 numéros. Les combinaisons sont utilisées, ent

Multi-level preconditioner for solving the Navier-Stokes equations in hemodynamics applications

Dana Christen

We present a multi-level algorithm to approximate the inverse of the fluid block in a Navier-Stokes saddle-point matrix where the coarse level is defined as a restriction of the degrees of freedom to those of lower order finite elements. A one-level scheme involving P1 and P2 finite elements is studied in details and several transfer operators are compared by means of two reference problems. Numerical results show that restriction and prolongation operators based on L2 projection lead to faster GMRES convergence of the fluid part, for all the examined combinations of mesh size, time step and Reynolds number.

2013

Robust speech recognition based on multi-stream processing

Astrid Hagen

Despite sophisticated present day automatic speech recognition (ASR) techniques, a single recognizer is usually incapable of accounting for the varying conditions in a typical natural environment. Higher robustness to a range of noise cases can potentially be achieved by combining the results of several recognizers operating in parallel. One such approach is multi-band processing, mimicking parallel processing of frequency subbands in human speech recognition as had been claimed by Fletcher. However, recent findings in both human and automatic speech recognition have revealed insufficiencies, such as the assumption of independence between frequency subbands, of the original multi-band ASR approach which often leads to reduced performance in the case of clean speech and wide-band noise. To overcome this problem, we propose and investigate a new set of "full combination" rules which integrate acoustic models trained on all possible combinations of subbands, preserving correlation information and leading to higher performance in all noise conditions. In this development, particular attention was given to the theoretical basis for all of the rules developed in terms of statistical theory, so that the assumptions that were necessary in each model become clear. The new combination strategies are developed for both posterior- and likelihood-based systems. These new combination strategies are then also applied to the combination of diverse feature streams, for example derived from multi-time scale analysis, which results in better exploitation of the often used instantaneous and time difference features. While combination may give the same weight to each expert, robustness of a multiple stream system can be further enhanced when each stream expert is assigned a weight reflecting its reliability. The new combination techniques are tested with several fixed and adaptive weighting strategies, including relative frequency of correct classification, least mean squared error, local signal-to-noise ratio, and maximum-likelihood based weights. We will see how the new multi-band approaches, which are consistently trained in clean speech, outperform original multi-band ASR models in both clean and noisy speech. Multi-band processing improves over the baseline fullband recognizer only in the case of narrow-band noise. However, combining multiple data streams from different time scales, using the same "full combination" rules, has also shown to significantly improve over the baseline in wide-band factory noise.

EPFL2002

Robust speech recognition based on multi-stream processing

Astrid Hagen

full combination'' rules which integrate acoustic models trained on all possible combinations of subbands, preserving correlation information and leading to higher performance in all noise conditions. In this development, particular attention was given to the theoretical basis for all of the rules developed in terms of statistical theory, so that the assumptions that were necessary in each model become clear. The new combination strategies are developed for both posterior- and likelihood-based systems. These new combination strategies are then also applied to the combination of diverse feature streams, for example derived from multi-time scale analysis, which results in better exploitation of the often used instantaneous and time difference features. While combination may give the same weight to each expert, robustness of a multiple stream system can be further enhanced when each stream expert is assigned a weight reflecting its reliability. The new combination techniques are tested with several fixed and adaptive weighting strategies, including relative frequency of correct classification, least mean squared error, local signal-to-noise ratio, and maximum-likelihood based weights. We will see how the new multi-band approaches, which are consistently trained in clean speech, outperform original multi-band ASR models in both clean and noisy speech. Multi-band processing improves over the baseline fullband recognizer only in the case of narrow-band noise. However, combining multiple data streams from different time scales, using the same

full combination'' rules, has also shown to significantly improve over the baseline in wide-band factory noise.

École Polytechnique Fédérale de Lausanne2001

Robust speech recognition based on multi-stream processing

Astrid Hagen

EPFL2002

Robust speech recognition based on multi-stream processing

Astrid Hagen

full combination'' rules which integrate acoustic models trained on all possible combinations of subbands, preserving correlation information and leading to higher performance in all noise conditions. In this development, particular attention was given to the theoretical basis for all of the rules developed in terms of statistical theory, so that the assumptions that were necessary in each model become clear. The new combination strategies are developed for both posterior- and likelihood-based systems. These new combination strategies are then also applied to the combination of diverse feature streams, for example derived from multi-time scale analysis, which results in better exploitation of the often used instantaneous and time difference features. While combination may give the same weight to each expert, robustness of a multiple stream system can be further enhanced when each stream expert is assigned a weight reflecting its reliability. The new combination techniques are tested with several fixed and adaptive weighting strategies, including relative frequency of correct classification, least mean squared error, local signal-to-noise ratio, and maximum-likelihood based weights. We will see how the new multi-band approaches, which are consistently trained in clean speech, outperform original multi-band ASR models in both clean and noisy speech. Multi-band processing improves over the baseline fullband recognizer only in the case of narrow-band noise. However, combining multiple data streams from different time scales, using the same

full combination'' rules, has also shown to significantly improve over the baseline in wide-band factory noise.

École Polytechnique Fédérale de Lausanne2001