Disease subtyping has been a critical aim of precision and personalized medicine. With the potential to improve patient outcomes, unsupervised and semi-supervised methods for determining phenotypes of subtypes have emerged with a recent focus on matrix and tensor factorization. However, interpretability of proposed models is debatable. Principal component analysis (PCA), a traditional method of dimensionality reduction, does not impose non-negativity constraints. Thus coefficients of the principal components are, in cases, difficult to translate to real physical units. Non-negative matrix factorization (NMF) constrains the factorization to positive numbers such that representative types resulting from the factorization are additive. Archetypal analysis (AA) extends this idea and seeks to identify pure types, archetypes, at the extremes of the data from which all other data can be expressed as a convex combination, or by proportion, of the archetypes. Using AA, this study sought to evaluate the sufficiency of AKI staging criteria through unsupervised subtyping. Archetype analysis failed to find a direct 1:1 mapping of archetypes to physician staging and also did not provide additional insight into patient outcomes. Several factors of the analysis such as quality of the data source and the difficulty in selecting features contributed to the outcome. Additionally, after performing feature selection with lasso across data subsets, it was determined that current staging criteria is sufficient to determine patient phenotype with serum creatinine at time of diagnosis to be a necessary factor.

La thèse se concentre sur une recherche méthodologique sur l'optimisation structurelle catégorielle au moyen d'un apprentissage multiple. Dans cette thèse, les variables catégorielles non ordinales sont traitées comme des variables discrètes multidimensionnelles. Afin de réduire la dimensionnalité, les nombreuses techniques d'apprentissage sont introduites pour trouver la dimensionnalité intrinsèque et mapper l'espace de conception d'origine sur un espace d'ordre réduit. Les mécanismes des techniques d'apprentissage à la fois linéaires et non linéaires sont d'abord étudiés. Ensuite, des exemples numériques sont testés pour comparer les performances de nombreuses techniques d’apprentissage. Sur la base de la représentation d'ordre réduit obtenue par Isomap, les opérateurs de mutation et de croisement évolutifs basés sur les graphes sont proposés pour traiter des problèmes d'optimisation structurelle catégoriels, notamment la conception du dôme, du cadre rigide de six étages et des structures en forme de dame. Ensuite, la méthode de recherche continue consistant à déplacer des asymptotes est exécutée et fournit une solution compétitive, mais inadmissible, en quelques rares itérations. Ensuite, lors de la deuxième étape, une stratégie de recherche discrète est proposée pour rechercher de meilleures solutions basées sur la recherche de voisins. Afin de traiter le cas dans lequel les instances de conception catégorielles sont réparties sur plusieurs variétés, nous proposons une méthode d'apprentissage des variétés k-variétés basée sur l'analyse en composantes principales pondérées. / The thesis concentrates on a methodological research on categorical structural optimizationby means of manifold learning. The main difficulty of handling the categorical optimization problems lies in the description of the categorical variables: they are presented in a category and do not have any orders. Thus the treatment of the design space is a key issue. In this thesis, the non-ordinal categorical variables are treated as multi-dimensional discrete variables, thus the dimensionality of corresponding design space becomes high. In order to reduce the dimensionality, the manifold learning techniques are introduced to find the intrinsic dimensionality and map the original design space to a reduced-order space. The mechanisms of both linear and non-linear manifold learning techniques are firstly studied. Then numerical examples are tested to compare the performance of manifold learning techniques mentioned above. It is found that the PCA and MDS can only deal with linear or globally approximately linear cases. Isomap preserves the geodesic distances for non-linear manifold however, its time consuming is the most. LLE preserves the neighbour weights and can yield good results in a short time. KPCA works like a non-linear classifier and we proves why it cannot preserve distances or angles in some cases. Based on the reduced-order representation obtained by Isomap, the graph-based evolutionary crossover and mutation operators are proposed to deal with categorical structural optimization problems, including the design of dome, six-story rigid frame and dame-like structures. The results show that the proposed graph-based evolutionary approach constructed on the reduced-order space performs more efficiently than traditional methods including simplex approach or evolutionary approach without reduced-order space. In chapter 5, the LLE is applied to reduce the data dimensionality and a polynomial interpolation helps to construct the responding surface from lower dimensional representation to original data. Then the continuous search method of moving asymptotes is executed and yields a competitively good but inadmissible solution within only a few of iteration numbers. Then in the second stage, a discrete search strategy is proposed to find out better solutions based on a neighbour search. The ten-bar truss and dome structural design problems are tested to show the validity of the method. In the end, this method is compared to the Simulated Annealing algorithm and Covariance Matrix Adaptation Evolutionary Strategy, showing its better optimization efficiency. In chapter 6, in order to deal with the case in which the categorical design instances are distributed on several manifolds, we propose a k-manifolds learning method based on the Weighted Principal Component Analysis. And the obtained manifolds are integrated in the lower dimensional design space. Then the method introduced in chapter 4 is applied to solve the ten-bar truss, the dome and the dame-like structural design problems.

Το ερευνητικό αντικείμενο της συγκεκριμένης διατριβής αναφέρεται στην επεξεργασία έγχρωμης εικόνας με χρήση της θεωρίας γράφων, την ανάκτηση εικόνας καθώς και την οργάνωση / διαχείριση βάσεων δεδομένων με μεθόδους γραφημάτων και αναγνώρισης προτύπων, με εφαρμογή σε πολυμέσα. Τα συγκεκριμένα προβλήματα προσεγγίστηκαν διατηρώντας τη γενικότητά τους και επιλύθηκαν με βάση τα ακόλουθα σημεία: 1. Ανάπτυξη τεχνικών για την επιλογή χαρακτηριστικών από τις εικόνες βάσει χαρακτηριστικών χαμηλού επιπέδου (χρώματος και υφής), για χρήση τους σε εφαρμογές ομοιότητας και ανάκτησης εικόνας. 2. Υπολογισμός μετρικών και αποστάσεων στο χώρο των χαρακτηριστικών. 3. Μελέτη της πολυσχιδούς δομής των εικόνων μιας βάσης στο χώρο των χαρακτηριστικών. 4. Ελάττωση της διάστασης του χώρου και παραγωγή αναπαραστάσεων δύο διαστάσεων. 5. Εφαρμογή των μεθόδων αυτών σε υποκειμενικές αποστάσεις εικόνων. Η θεωρία γράφων και οι μέθοδοι αναγνώρισης προτύπων χρησιμοποιήθηκαν προκειμένου να παρουσιαστούν βέλτιστες λύσεις αφενός στο πρόβλημα της ανάκτησης εικόνων από βάσεις δεδομένων και αφετέρου στην οργάνωση και διαχείριση τέτοιων βάσεων εικόνων. Η διατριβή φέρνει πιο κοντά την επεξεργασία εικόνας με μεθόδους προερχόμενες από τη θεωρία γραφημάτων, τη στατιστική και την αναγνώριση προτύπων. Σε όλη τη διάρκεια της διατριβής, ιδιαίτερη έμφαση δόθηκε στο ζήτημα της εύρεσης του κατάλληλου συνδυασμού μεταξύ της αποτελεσματικότητας των συστημάτων και της αποδοτικότητας στα πλαίσια της εφαρμογής των προτεινόμενων αλγοριθμικών διαδικασιών. Τα αναλυτικά πειραματικά αποτελέσματα που πραγματοποιήθηκαν, αποδεικνύουν την βελτιωμένη απόδοση των προτεινόμενων μεθοδολογιών. / The subject of this doctoral thesis is related to color image processing using graph theoretic methods, image retrieval and image database management and organization in the reduced feature space, using pattern recognition analysis, with multimedia applications. The author attempted to approach the thesis subject by retaining its genericness and addressing the following points: 1. Development of techniques for extraction of image visual attributes based on low level features (color and texture information), to be used for image similarity and retrieval practices. 2. Calculation of metrics and distances in the feature space. 3. Study of the image manifolds created in the selected feature space. 4. Application of dimensionality reduction techniques and production of biplots. 5. Application of the proposed methodologies using perceptual image distances. Graph theory and pattern recognition methodologies were incorporated in order to provide novel solution to color image retrieval of image databases, as well as to image database management and organization. The current thesis brings closer image processing with graph theoretic methodologies, statistical analysis and pattern recognition. Throughout the thesis, consideration has been taken for finding the best trade off between effectiveness and efficiency when applying the proposed algorithmic procedures. The extended experimental results carried out in all stages of the projected studies reveal the enhanced performance of the proposed methodologies.

<p dir="ltr">Deep Neural Networks (DNNs) successfully perform object detection tasks, and the Con- volutional Neural Network (CNN) backbone is a commonly used feature extractor before secondary tasks such as detection, classification, or segmentation. In a DNN model, the relationship between the features learned by the model from the training data and the features leveraged by the model during test and deployment has motivated the area of feature interpretability studies. The work presented here applies equally to white-box and black-box models and to any DNN architecture. The metrics developed do not require any information beyond the feature vector generated by the feature extraction backbone. These methods are therefore the first methods capable of estimating black-box model robustness in terms of latent space complexity and the first methods capable of examining feature representations in the latent space of black box models.</p><p dir="ltr">This work contributes the following four novel methodologies and results. First, a method for quantifying the invariance and/or equivariance of a model using the training data shows that the representation of a feature in the model impacts model performance. Second, a method for quantifying an observed domain gap in a dataset using the latent feature vectors of an object detection model is paired with pixel-level augmentation techniques to close the gap between real and synthetic data. This results in an improvement in the model’s F1 score on a test set of outliers from 0.5 to 0.9. Third, a method for visualizing and quantifying similarities of the latent manifolds of two black-box models is used to correlate similar feature representation with increase success in the transferability of gradient-based attacks. Finally, a method for examining the global complexity of decision boundaries in black-box models is presented, where more complex decision boundaries are shown to correlate with increased model robustness to gradient-based and random attacks.</p>