Parametric Local Metric Learning for Nearest Neighbor Classification

We study the problem of learning local metrics for nearest neighbor classification. Most previous works on local metric learning learn a number of local unrelated metrics. While this "independence" approach delivers an increased flexibility its downside is the considerable risk of overfitting. We present a new parametric local metric learning method in which we learn a smooth metric matrix function over the data manifold. Using an approximation error bound of the metric matrix function we learn local metrics as linear combinations of basis metrics defined on anchor points over different regions of the instance space. We constrain the metric matrix function by imposing on the linear combinations manifold regularization which makes the learned metric matrix function vary smoothly along the geodesics of the data manifold. Our metric learning method has excellent performance both in terms of predictive power and scalability. We experimented with several large-scale classification problems, tens of thousands of instances, and compared it with several state of the art metric learning methods, both global and local, as well as to SVM with automatic kernel selection, all of which it outperforms in a significant manner

Distance and kernel based learning over composite representations

The goal of this dissertation is to examine various aspects of the distance- and kernel-based learning paradigms applied in relational settings. We start by introducing a multi-relational representation formalism, at the core of which lie the concepts of tuples, sets and lists, which we implemented over the relational algebra language. By combining these data types we are able to model a variety of composite objects, such as trees and graphs. We proceed with the definition of various distance and kernel operators over the representation formalism. We are not constrained to a specific operator, instead, we are free to assign an operator, selected from a set of available operators, to a particular data type. The final operator over the composite objects is given as a recursive combination of operators assigned to the sub-structures which constitute the objects. We focus on mapping-based operators defined over sets. Next, we propose three new and flexible families of set kernels where the overall similarity is based on mappings between the elements of the two sets. These kernels differ from most of the existing set kernels which are based on averaging of the similarities of all the elements of the two sets. Finally, we propose a general framework for adaptively selecting representations of complex data and/or operators over representations. More precisely, our framework assumes a set of predefined representations and operators which are then combined in an optimal way. We focus only on the distance-based paradigm and we exploit previous work on metric learning over vectorial data. We use the optimal combination of different graph decompositions into substructures of specific types to define adaptive graph kernels which address the limitations of the existing kernels over these complex structures. We undertook extensive comparisons of our distance- and kernel-based relational system, which included: an empirical evaluation of various composite distances, with the focus on comparison of set distances based on mappings; an empirical evaluation of different complex kernels, with the focus on comparison of set kernels based on averaging and set kernels based on various mappings; an empirical evaluation of our adaptive framework for the tasks of combination of set distances, and combination of various graph decompositions into substructures of various types. The empirical evaluation of the system has shown that the proposed distance- and kernel-based paradigms are effective over a number of relational benchmark datasets. Additionally, in all of the examined relational problems we achieved state-of-the-art results which are better than the best results obtained using other relational systems

Learning to Combine Distances for Complex Representations

The k-Nearest Neighbors algorithm can be easily adapted to classify complex objects (e.g. sets, graphs) as long as a proper dissimilarity function is given over an input space. Both the representation of the learning instances and the dissimilarity employed on that representation should be determined on the basis of domain knowledge. However, even in the presence of domain knowledge, it can be far from obvious which complex representation should be used or which dissimilarity should be applied on the chosen representation. In this paper we present a framework that allows to combine different complex representations of a given learning problem and/or different dissimilarities defined on these representations. We build on ideas developed previously on metric learning for vectorial data. We demonstrate the utility of our method in domains in which the learning instances are represented as sets of vectors by learning how to combine different set distance measures. 1

Méthodes et modèles pour l'évaluation des conséquences de la rupture d'une structure en béton armé sous l'action d'un souffle

Ce travail est consacré à l'étude des différentes étapes du processus engendré par l'explosion et les effets mécaniques qu'elle produit. Pour ce faire, on caractérise : l'onde de pression issue d'une détonation en milieu aérien, l'espace d'expansion du champ de pression et son interaction avec une structure, les lois de comportement des matériaux et leur représentation dans les codes numériques. Des équations empiriques conçues pour prévoir les charges issues de détonations dans un milieu libre et confiné sont validées. La pertinence d'une hypothèse concernant les valeurs de la pression réfléchie d'un mur rigide lors d'une explosion est analysée. En outre, on propose un modèle simplifié du comportement de béton basé sur des contraintes équivalentes prenant en compte des modifications des propriétés mécaniques au cours des déformations. La comparaison des résultats numériques de calcul d'une plaque en béton armé soumise à une onde de choc est présentée via différents modèles constitutifs du béton.ORLEANS-BU Sciences (452342104) / SudocSudocFranceF

Model mining for robust feature selection

A common problem with most of the feature selection methods is that they often produce feature sets--models--that are not stable with respect to slight variations in the training data. Different authors tried to improve the feature selection stability using ensemble methods which aggregate different feature sets into a single model. However, the existing ensemble feature selection methods suffer from two main shortcomings: (i) the aggregation treats the features independently and does not account for their interactions, and (ii) a single feature set is returned, nevertheless, in various applications there might be more than one feature sets, potentially redundant, with similar information content. In this work we address these two limitations. We present a general framework in which we mine over different feature models produced from a given dataset in order to extract patterns over the models. We use these patterns to derive more complex feature model aggregation strategies that account for feature interactions, and identify core and distinct feature models. We conduct an extensive experimental evaluation of the proposed framework where we demonstrate its effectiveness over a number of high-dimensional problems from the fields of biology and text-mining