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The performance of machine learning and pattern recognition algorithms generally depends on data representation. That is why, much of the current effort in performing machine learning algorithms goes into the design of preprocessing frameworks and data transformations able to support effective machine learning. The method proposed in this work consists of a hybrid linear feature extraction scheme to be used in supervised multi-class classification problems. Inspired by two recent linear discriminant methods: robust sparse linear discriminant analysis (RSLDA) and inter-class sparsity-based discriminative least square regression (ICS_DLSR), we propose a unifying criterion that is able to retain the advantages of these two powerful methods. The resulting transformation relies on sparsity-promoting techniques both to select the features that most accurately represent the data and to preserve the row-sparsity consistency property of samples from the same class. The linear transformation and the orthogonal matrix are estimated using an iterative alternating minimization scheme based on steepest descent gradient method and different initialization schemes. The proposed framework is generic in the sense that it allows the combination and tuning of other linear discriminant embedding methods. According to the experiments conducted on several datasets including faces, objects, and digits, the proposed method was able to outperform competing methods in most cases.

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Dans ce papier, nous avons développé un algorithme d'hybridation (recalage) de la navigation inertielle, noté Q-SUKF, qui combine le filtre de Kalman sans parfum à paramètre (SUKF) et l'utilisation des propriétés de rotation et d'unicité des quaternions (Q) pour représenter l'attitude. L'utilisation des quaternions unités dans le calcul de la matrice de covariance d'erreurs prédite empêche les problèmes de singularité et la dérive des informations d'attitude. L'augmentation de l'incertitude dans les angles d'attitude, est modélisé par un vecteur de rotation pour garantir que la normalisation du quaternion est toujours maintenue dans le filtre. Le Q-SUKF proposé est bien adapté pour estimer récursivement les états de la navigation, quelque soient les valeurs initiales sur les angles d'attitude ou la dynamique des mouvements du mobile, à l'aide des capteurs externes qui sont complémentaires et/ou redondants.