High dimensional, low sample, data have singular sample covariance matrices,rendering them impossible to analyse by regular canonical correlation (CC). Byusing random subspace method (RSM) calculation of canonical correlation be-comes possible, and a Monte Carlo analysis shows resulting maximal CC canreliably distinguish between data with true correlation (above 0.5) and with-out. Statistics gathered from RSMCCA can be used to model true populationcorrelation by beta regression, given certain characteristic of data set. RSM-CCA applied on real biological data however show that the method can besensitive to deviation from normality and high degrees of multi-collinearity.

[pt] Hoje em dia, grande parte do conhecimento acumulado está armazenada em forma de dados. Dentre as ferramentas capazes de atuar como modelos representativos de sistemas reais, os Sistemas de Inferência Fuzzy têm se destacado pela capacidade de fornecer modelos precisos e, ao mesmo tempo, interpretáveis. A interpretabilidade é obtida a partir de regras linguísticas, que podem ser extraídas de bases de dados bases históricas e que permitem ao usuário compreender a relação entre as variáveis do problema. Entretanto, tais sistemas sofrem com a maldição da dimensionalidade ao lidar com problemas complexos, isto é, com um grande número de variáveis de entrada ou padrões, gerando problemas de escalabilidade. Esta dissertação apresenta um novo algoritmo de geração automática de regras, denominado RandomFIS, especificamente para problemas de classificação, capaz de lidar com grandes bases de dados tanto em termos de número de variáveis de entrada (atributos) quanto em termos de padrões (instâncias). O modelo RandomFIS utiliza os conceitos de seleção de variáveis (Random Subspace) e Bag of Little Bootstrap (BLB), que é uma versão escalável do Bootstrapping, criando uma estrutura de comitê de classificadores. O RandomFIS é avaliado em várias bases benchmark, demostrando ser um modelo robusto que mantém a interpretabilidade e apresenta boa acurácia mesmo em problemas envolvendo grandes bases de dados. / [en] Nowadays, much of the accumulated knowledge is stored as data. Among the tools capable of acting as representative models of real systems, Fuzzy Inference Systems are recognized by their ability to provide accurate and at the same time interpretable models. Interpretability is obtained from linguistic rules, which can be extracted from historical databases. These rules allow the end user to understand the relationship between variables in a specific problem. However, such systems experience the curse of dimensionality when handling complex problems, i.e. with a large number of input variables or patterns in the dataset, giving origin to scalability issues. This dissertation presents a new algorithm for automatic generation of fuzzy rules, called RandomFIS, specifically for classification problems, which is able to handle large databases both in terms of number of input variables (attributes) and in terms of patterns (instances). The RandomFIS model makes use of feature selection concepts (Random Subspace) and Bag of Little Bootstrap (BLB), which is a scalable version of Bootstrapping, creating a classifier committee structure. RandomFIS is tested in several benchmark datasets and shows to be a robust model that maintains interpretability and good accuracy even in problems involving large databases.

Dans cette thèse, nous proposons plusieurs nouvelles techniques pour la classification d'images hyperspectrales basées sur l'apprentissage d'ensemble. Le cadre proposé introduit des innovations importantes par rapport aux approches précédentes dans le même domaine, dont beaucoup sont basées principalement sur un algorithme individuel. Tout d'abord, nous proposons d'utiliser la Forêt de Rotation (Rotation Forest) avec différentes techiniques d'extraction de caractéristiques linéaire et nous comparons nos méthodes avec les approches d'ensemble traditionnelles, tels que Bagging, Boosting, Sous-espace Aléatoire et Forêts Aléatoires. Ensuite, l'intégration des machines à vecteurs de support (SVM) avec le cadre de sous-espace de rotation pour la classification de contexte est étudiée. SVM et sous-espace de rotation sont deux outils puissants pour la classification des données de grande dimension. C'est pourquoi, la combinaison de ces deux méthodes peut améliorer les performances de classification. Puis, nous étendons le travail de la Forêt de Rotation en intégrant la technique d'extraction de caractéristiques locales et l'information contextuelle spatiale avec un champ de Markov aléatoire (MRF) pour concevoir des méthodes spatio-spectrale robustes. Enfin, nous présentons un nouveau cadre général, ensemble de sous-espace aléatoire, pour former une série de classifieurs efficaces, y compris les arbres de décision et la machine d'apprentissage extrême (ELM), avec des profils multi-attributs étendus (EMaPS) pour la classification des données hyperspectrales. Six méthodes d'ensemble de sous-espace aléatoire, y compris les sous-espaces aléatoires avec les arbres de décision, Forêts Aléatoires (RF), la Forêt de Rotation (RoF), la Forêt de Rotation Aléatoires (Rorf), RS avec ELM (RSELM) et sous-espace de rotation avec ELM (RoELM), sont construits par multiples apprenants de base. L'efficacité des techniques proposées est illustrée par la comparaison avec des méthodes de l'état de l'art en utilisant des données hyperspectrales réelles dans de contextes différents. / In this thesis, we propose several new techniques for the classification of hyperspectral remote sensing images based on multiple classifier system (MCS). Our proposed framework introduces significant innovations with regards to previous approaches in the same field, many of which are mainly based on an individual algorithm. First, we propose to use Rotation Forests with several linear feature extraction and compared them with the traditional ensemble approaches, such as Bagging, Boosting, Random subspace and Random Forest. Second, the integration of the support vector machines (SVM) with Rotation subspace framework for context classification is investigated. SVM and Rotation subspace are two powerful tools for high-dimensional data classification. Therefore, combining them can further improve the classification performance. Third, we extend the work of Rotation Forests by incorporating local feature extraction technique and spatial contextual information with Markov random Field (MRF) to design robust spatial-spectral methods. Finally, we presented a new general framework, Random subspace ensemble, to train series of effective classifiers, including decision trees and extreme learning machine (ELM), with extended multi-attribute profiles (EMAPs) for classifying hyperspectral data. Six RS ensemble methods, including Random subspace with DT (RSDT), Random Forest (RF), Rotation Forest (RoF), Rotation Random Forest (RoRF), RS with ELM (RSELM) and Rotation subspace with ELM (RoELM), are constructed by the multiple base learners. The effectiveness of the proposed techniques is illustrated by comparing with state-of-the-art methods by using real hyperspectral data sets with different contexts.