In recent years, deep neural network models have shown to outperform many state of the art algorithms. The reason for this is, unsupervised pretraining with multi-layered deep neural networks have shown to learn better features, which further improves many supervised tasks. These models not only automate the feature extraction process but also provide with robust features for various machine learning tasks. But the unsupervised pretraining and feature extraction using multi-layered networks are restricted only to the input features and not to the output. The performance of many supervised learning algorithms (or models) depends on how well the output dependencies are handled by these algorithms [Dembczy´nski et al., 2012]. Adapting the standard neural networks to handle these output dependencies for any specific type of problem has been an active area of research [Zhang and Zhou, 2006, Ribeiro et al., 2012]. On the other hand, inference into multimodal data is considered as a difficult problem in machine learning and recently ‘deep multimodal neural networks’ have shown significant results [Ngiam et al., 2011, Srivastava and Salakhutdinov, 2012]. Several problems like classification with complete or missing modality data, generating the missing modality etc., are shown to perform very well with these models. In this work, we consider three nontrivial supervised learning tasks (i) multi-class classification (MCC), (ii) multi-label classification (MLC) and (iii) label ranking (LR), mentioned in the order of increasing complexity of the output. While multi-class classification deals with predicting one class for every instance, multi-label classification deals with predicting more than one classes for every instance and label ranking deals with assigning a rank to each label for every instance. All the work in this field is associated around formulating new error functions that can force network to identify the output dependencies. Aim of our work is to adapt neural network to implicitly handle the feature extraction (dependencies) for output in the network structure, removing the need of hand crafted error functions. We show that the multimodal deep architectures can be adapted for these type of problems (or data) by considering labels as one of the modalities. This also brings unsupervised pretraining to the output along with the input. We show that these models can not only outperform standard deep neural networks, but also outperform standard adaptations of neural networks for individual domains under various metrics over several data sets considered by us. We can observe that the performance of our models over other models improves even more as the complexity of the output/ problem increases.

De nombreux phénomènes naturels sont trop complexes pour être pleinement reconnus par un seul instrument de mesure ou par une seule modalité. Par conséquent, le domaine de recherche de la multi-modalité a émergé pour mieux identifier les caractéristiques riches du phénomène naturel de la multi-propriété naturelle, en analysant conjointement les données collectées à partir d’uniques modalités, qui sont en quelque sorte complémentaires. Dans notre étude, le phénomène d’intérêt multi-propriétés est l’activité du cerveau humain et nous nous intéressons à mieux la localiser au moyen de ses propriétés électromagnétiques, mesurables de manière non invasive. En neurophysiologie, l’électroencéphalographie (EEG) et la magnétoencéphalographie (MEG) constituent un moyen courant de mesurer les propriétés électriques et magnétiques de l’activité cérébrale. Notre application dans le monde réel, à savoir le problème de reconstruction de source EEG / MEG, est un problème fondamental en neurosciences, allant des sciences cognitives à la neuropathologie en passant par la planification chirurgicale. Considérant que le problème de reconstruction de source EEG /MEG peut être reformulé en un système d’équations linéaires sous-déterminé, la solution (l’activité estimée de la source cérébrale) doit être suffisamment parcimonieuse pour pouvoir être récupérée de manière unique. La quantité de parcimonie est déterminée par les conditions dites de récupération. Cependant, dans les problèmes de grande dimension, les conditions de récupération conventionnelles sont extrêmement strictes. En regroupant les colonnes cohérentes d’un dictionnaire, on pourrait obtenir une structure plus incohérente. Cette stratégie a été proposée en tant que cadre d’identification de structure de bloc, ce qui aboutit à la segmentation automatique de l’espace source du cerveau, sans utiliser aucune information sur l’activité des sources du cerveau et les signaux EEG / MEG. En dépit du dictionnaire structuré en blocs moins cohérent qui en a résulté, la condition de récupération conventionnelle n’est plus en mesure de calculer la caractérisation de la cohérence. Afin de relever le défi mentionné, le cadre général des conditions de récupération exactes par bloc-parcimonie, comprenant trois conditions théoriques et une condition dépendante de l’algorithme, a été proposé. Enfin, nous avons étudié la multi-modalité EEG et MEG et montré qu’en combinant les deux modalités, des régions cérébrales plus raffinées sont apparues / Three main challenges have been addressed in this thesis, in three chapters.First challenge is about the ineffectiveness of some classic methods in high-dimensional problems. This challenge is partially addressed through the idea of clustering the coherent parts of a dictionary based on the proposed characterisation, in order to create more incoherent atomic entities in the dictionary, which is proposed as a block structure identification framework. The more incoherent atomic entities, the more improvement in the exact recovery conditions. In addition, we applied the mentioned clustering idea to real-world EEG/MEG leadfields to segment the brain source space, without using any information about the brain sources activity and EEG/MEG signals. Second challenge raises when classic recovery conditions cannot be established for the new concept of constraint, i.e., block-sparsity. Therefore, as the second research orientation, we developed a general framework for block-sparse exact recovery conditions, i.e., four theoretical and one algorithmic-dependent conditions, which ensure the uniqueness of the block-sparse solution of corresponding weighted mixed-norm optimisation problem in an underdetermined system of linear equations. The mentioned generality of the framework is in terms of the properties of the underdetermined system of linear equations, extracted dictionary characterisations, optimisation problems, and ultimately the recovery conditions. Finally, the combination of different information of a same phenomenon is the subject of the third challenge, which is addressed in the last part of dissertation with application to brain source space segmentation. More precisely, we showed that by combining the EEG and MEG leadfields and gaining the electromagnetic properties of the head, more refined brain regions appeared.