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Thesis Reference Thesis Nonlinear transform learning: model, applications and algorithms KOSTADINOV, Dimche Abstract Les principes de la modélisation de non-linéarités sont essentiels pour maints problèmes de la vie réelle. Leur traitement joue un rôle central et influence non seulement la qualité de la solution, mais aussi la complexité computationnelle et les gains dans les compromis possiblement impliqués, qui sont tous hautement demandés dans une variété d’applications, comme la prise du contenu des empreintes digitales active, la reconstitution des images, l’apprentissage supervisé et non-supervisé des représentations discriminatives pour des tâches de reconnaissance d’image et les méthodes de regroupement. Dans la thèse présente un modèle de transformation non-linéaire généralisé novateur est proposé et étudié. Notre intérêt principal et élément de base est la transformation non linéaire exprimée par une double opération qui consiste en une modélisation linéaire suivi d’une non-linéarité par éléments. Pour ce faire, selon l’application considérée, des interprétations probabilistes sont développées et des généralisations et des cas particuliers sont proposées et [...] Reference KOSTADINOV, Dimche. Nonlinear transform learning: model, applications and algorithms. Thèse de doctorat : Univ. Genève, 2018, no. Sc. 5335 URN : urn:nbn:ch:unige-1185338 DOI : 10.13097/archive-ouverte/unige:118533 Available at: http://archive-ouverte.unige.ch/unige:118533 Disclaimer: layout of this document may differ from the published version. 1 / 1 UNIVERSITÉ DE GENÈVE FACULTÉ DES SCIENCES Département d’Informatique Professeur S. Voloshynovskiy Nonlinear Transform Learning: Model, Applications and Algorithms THÈSE présentée à la Faculté des sciences de l’Université de Genève pour obtenir le grade de Docteur ès sciences, mention informatique par Dimche Kostadinov de Strumica (Macedonia) Thèse no 5335 GENÈVE Repro-Mail - Université de Genève 2018 NONLINEAR TRANSFORM LEARNING: MODEL, APPLICATIONS AND ALGORITHMS A DISSERTATION SUBMITTED TO THE DEPARTMENT OF COMPUTER SCIENCE OF UNIVERSITY OF GENEVA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Dimche Kostadinov May 2019 c Copyright by Dimche Kostadinov 2019 All Rights Reserved ii In memory of my father To all that I care about with love and eternal appreciation Acknowledgements I would like to thank my supervisor Prof. Sviatoslav Voloshynovskiy for providing me op- portunity to work on this PhD Thesis, all his encouragement, considerations and involvement at all times, the discussions, the insights and all the rest of his support. I would like to thank my jury members Prof. Karen Egiazarian, Prof. Teddy Furon, Prof. Sylvain Sardy and Prof. Stéphane Marchand-Maillet for their careful reading, valuable suggestions and comments. I would like to thank Taras Holotyak for his time spend in the discussions and reading of my draft concepts as well as providing valuable comments. I would like to thank Sohrab Ferdowsi for taking the time and participating in discussions regarding my presentations, elaborations and outlines of many of my ideas on the board in our office. I’m thankful to Maurits Diephuis for been involved in providing comments on the English writing over many papers. In addition, I would like to thank Behrooz Razeghi for his interests and enthusiasm in some of the concepts over several works and getting involved in providing comments towards certain details and clarifications. I want to mention all of the rest of my colleagues from our Stohastic Information Processing Group, who have directly or indirectly provided a support in terms of discussions, comments and suggestions related to the work in this Thesis. I would like to thank our head of the Computer Vision and Multimedia Laboratory Prof. Thierry Pun for outlying his supportive attitude and enabling a great working environment, as well as Prof. Stéphane Marchand-Maillet and Prof. Alexandros Kalousis for providing me with insights and suggestions related to some machine learning aspects. I would like to thank Fokko Beekhof and Farzad Farhadzadeh for their initial help during my relocation to Geneva. I would like to thank Boris Petrov Lambrev for providing me his help with the translation of the abstract. I would like to thank also the rest of the colleges of the Computer Vision and Multimedia Laboratory with whom I have spend a wonderful time, made professional as well as personal bonds. I’m thankful to many of the colleges with whom I had many coffee breaks with interesting and re-energizing conversations. I would like to thank Edgar Francisco Roman, Sohrab Ferdowsi, Ke Sun, Majid Yazdani and Michal Muszynski for the delightful accompany and the great hang outs. Finally, I would like to thank my mother, my two sisters and their families for their never-ending support and I would like to thank to my wife. Abstract Modeling of nonlinearities is essential for many real-world problems, where its treatment plays a central role and impacts not only the quality of the solution but also the computational complexity. Its high prevalence impacts on a variety of applications, including active content fingerprinting, image restoration, supervised and unsupervised discriminative representation learning for image recognition tasks and clustering. In this thesis, we introduce and study a novel generalized nonlinear transform model. In particular, our main focus and core element is on the nonlinear transform that is expressible by a two-step operation consisting of linear mapping, which is followed by element-wise nonlinearity. To that end, depending on the considered application, we unfold probabilistic interpretations, propose generalizations, extensions and take into account special cases. An approximation to the empirical likelihood of our nonlinear transform model provides a learning objective, where we not only identify and analyze the corresponding trade-offs, but we give information-theoretic as well as empirical risk connections considering the addressed objectives in the respective problem formulations. We introduce a generalization that extends an integrated maximum marginal principle over the approximation to the empirical likelihood, which allows us to address the optimal parameter estimation. In this scope, depending on the modeled assumptions w.r.t. an application objective, the implementation of the maximum marginal principle enables us to efficiently estimate the model parameters where we propose an approximate and exact closed form solutions as well as present iterative algorithms with convergence guarantees. Numerical experiments empirically validate the nonlinear transform model, the learning principle, and the algorithms for active content fingerprinting, image denoising, estimation of robust and discriminative nonlinear transform representation for image recognition tasks and our clustering method that is preformed in the nonlinear transform domain. At the moment of thesis preparation our numerical results demonstrate advantages in comparison to the state-of-the-art methods of the corresponding category, regarding the learning time, the run time and the quality of the solution. Résumé Les principes de la modélisation de non-linéarités sont essentiels pour maints problèmes de la vie réelle. Leur traitement joue un rôle central et influence non seulement la qualité de la solution, mais aussi la complexité computationnelle et les gains dans les compromis possiblement impliqués, qui sont tous hautement demandés dans une variété d’applications, comme la prise du contenu des empreintes digitales active, la reconstitution des images, l’apprentissage supervisé et non-supervisé des représentations discriminatives pour des tâches de reconnaissance d’image et les méthodes de regroupement. Dans la thèse présente un modèle de transformation non-linéaire généralisé novateur est proposé et étudié. Notre intérêt principal et élément de base est la transformation non linéaire exprimée par une double opération qui consiste en une modélisation linéaire suivi d’une non-linéarité par éléments. Pour ce faire, selon l’application considérée, des interprétations probabilistes sont développées et des généralisations et des cas particuliers sont proposées et considérées. Une approximation à la probabilité empirique de la transformation non-linéaire assure l’objectif d’apprentissage où non seulement les compromis correspondants sont identifiés et analysés, mais les connexions à risque d’un point de vue informative-théorique, ainsi qu’empirique sont proposé en considérant les objectifs adressés dans les formulations respec- tives du problème. L’introduction d’une généralisation qui étend un principe maximal intégré marginal sur l’approximation de la probabilité empirique permet d’adresser l’estimation optimale du paramètre. Dans cet esprit, selon les hypothèses modelées par rapport à un objectif d’application la réalisation du principe marginal maximal, permet d’estimer de manière efficace les paramètres du modèle où des solutions analytiques approximatives et exactes sont proposées, ainsi que des algorithmes itératifs avec des garanties convergentes. Des expériences numériques confirment la validité de notre modèle NT, le principe d’apprentissage, les algorithmes pour la prise du contenu des empreintes digitales active, l’enlèvement du bruit des images, l’estimation d’une représentation de transformation non- linéaire robuste et discriminative pour des tâches de reconnaissance d’image et la méthode de regroupement exécuté dans le domaine
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