The main contribution of this thesis is the concept of Fenchel duality with a focus on its application in the field of machine learning problems and image restoration tasks. We formulate a general optimization problem for modeling support vector machine tasks and assign a Fenchel dual problem to it, prove weak and strong duality statements as well as necessary and sufficient optimality conditions for that primal-dual pair. In addition, several special instances of the general optimization problem are derived for different choices of loss functions for both the regression and the classifification task. The convenience of these approaches is demonstrated by numerically solving several problems. We formulate a general nonsmooth optimization problem and assign a Fenchel dual problem to it. It is shown that the optimal objective values of the primal and the dual one coincide and that the primal problem has an optimal solution under certain assumptions. The dual problem turns out to be nonsmooth in general and therefore a regularization is performed twice to obtain an approximate dual problem that can be solved efficiently via a fast gradient algorithm. We show how an approximate optimal and feasible primal solution can be constructed by means of some sequences of proximal points closely related to the dual iterates. Furthermore, we show that the solution will indeed converge to the optimal solution of the primal for arbitrarily small accuracy. Finally, the support vector regression task is obtained to arise as a particular case of the general optimization problem and the theory is specialized to this problem. We calculate several proximal points occurring when using difffferent loss functions as well as for some regularization problems applied in image restoration tasks. Numerical experiments illustrate the applicability of our approach for these types of problems.

In der vorliegenden Dissertation wurde ein datengetriebenes Verfahren zum maschinellen Lernen von Mensch-Roboter Interaktionen auf Basis von Mensch-Mensch Demonstrationen entwickelt. Während einer Trainingsphase werden Bewegungen zweier Interakteure mittels Motion Capture erfasst und in einem Zwei-Personen Interaktionsmodell gelernt. Zur Laufzeit wird das Modell sowohl zur Erkennung von Bewegungen des menschlichen Interaktionspartners als auch zur Generierung angepasster Roboterbewegungen eingesetzt. Die Leistungsfähigkeit des Ansatzes wird in drei komplexen Anwendungen evaluiert, die jeweils kontinuierliche Bewegungskoordination zwischen Mensch und Roboter erfordern. Das Ergebnis der Dissertation ist ein Lernverfahren, das intuitive, zielgerichtete und sichere Kollaboration mit Robotern ermöglicht.

Machine Learning interatomic potentials (ML-IAP) are currently the most promising Non-empirical IAPs for molecular dynamic (MD) simulations. They use Machine Learning (ML) methods to fit the potential energy surface (PES) with large reference datasets of the atomic configurations and their corresponding properties. Promising near quantum mechanical accuracy while being orders of magnitudes faster than first principle methods, ML-IAPs are the new “hot topic” in material science research. Unfortunately, most of the available publications require advanced knowledge about ML methods and IAPs, making them hard to understand for beginners and outsiders. This work serves as a plain introduction, providing all the required knowledge about IAPs, ML, and ML-IAPs from the beginning and giving an overview of the most relevant approaches and concepts for building those potentials. Exemplary a gaussian approximation potential (GAP) for amorphous carbon is used to simulate the defect induced deformation of carbon nanotubes. Comparing the results with published density-functional tight-binding (DFTB) results and own Empirical IAP MD-simulations shows that publicly available ML-IAP can already be used for simulation, being indeed faster than and nearly as accurate as first-principle methods. For the future two main challenges appear: First, the availability of ML-IAPs needs to be improved so that they can be easily used in the established MD codes just as the Empirical IAPs. Second, an accurate characterization of the bonds represented in the reference dataset is needed to assure that a potential is suitable for a special application, otherwise making it a 'black-box' method.:1 Introduction 2 Molecular Dynamics 2.1 Introduction to Molecular Dynamics 2.2 Interatomic Potentials 2.2.1 Development of PES 3 Machine Learning Methods 3.1 Types of Machine Learning 3.2 Building Machine Learning Models 3.2.1 Preprocessing 3.2.2 Learning 3.2.3 Evaluation 3.2.4 Prediction 4 Machine Learning for Molecular Dynamics Simulation 4.1 Definition 4.2 Machine Learning Potentials 4.2.1 Neural Network Potentials 4.2.2 Gaussian Approximation Potential 4.2.3 Spectral Neighbor Analysis Potential 4.2.4 Moment Tensor Potentials 4.3 Comparison of Machine Learning Potentials 4.4 Machine Learning Concepts 4.4.1 On the fly 4.4.2 De novo Exploration 4.4.3 PES-Learn 5 Simulation of defect induced deformation of CNTs 5.1 Methodology 5.2 Results and Discussion 6 Conclusion and Outlook 6.1 Conclusion 6.2 Outlook

Alternative Geschäftsmodelle wie Software as a Service (SaaS) und Open-Source-Software (OSS) steigern die Attraktivität von Enterprise Resource Planning (ERP) Systemen für Kleine und Mittelständische Unternehmen (KMU). Jedoch stellen die Beratungsleistungen, die für die Konfiguration eines ERP-Systems zur Anpassung an die spezifischen Bedürfnisse eines Unternehmens notwendig sind, eine hohe Einführungshürde dar. Eine Konfigurationsoption, die bei vielen ERP-Systemen eine Rolle spielt, ist die Kategorienkonfiguration. Mit Hilfe einer automatisierten Konfigurationsunterstützung können Geschäftsführer von kleinen Unternehmen die Kategorienkonfiguration selbst durchführen und einen Teil der Einführungskosten einsparen. Im Rahmen der kumulativen Dissertation werden Automatisierungsansätze zur Konfigurationsunterstützung für die ERP-Kategorienkonfiguration generiert und auf das Open-Source ERP-System ERP5 angewandt. Die Automatisierungsansätze basieren auf Ähnlichkeitsberechnungen zu Falldatensätzen von 235 Unternehmen, Kategorien-Konsolidierung durch Umleitungsinformationen in Wikipedia-Artikeln, Templates und Meta-Templates. Die empirische Evaluation in einem Laborexperiment mit 100 Teilnehmern und eine Umfrage bestätigen die Gültigkeit, Nützlichkeit und Effektivität der generierten Ansätze. Die Konfigurationsunterstützung kann durch einen standardisierten Beratungsprozess und die Vermittlung des für eine konkrete ERP-Einführung notwendigen Wissens mittels Massenindividualisierung ergänzt werden. Dieser Ansatz wurde mit und für ERP5 umgesetzt und lässt sich auch auf andere Open-Source-Projekte übertragen.

In this thesis inhibition as a means for competition among neurons in an unsupervised learning system is studied. In the first part of the thesis, the role of inhibition in robustness against loss of information in the form of occlusion in visual data is investigated. In the second part, inhibition as a reason for loss of information in the mathematical models of neural system is addressed. In that part, a learning rule for modeling inhibition with lowered loss of information and also a dis-inhibitory system which induces a winner-take-all mechanism are introduced. The models used in this work are unsupervised feature extractors made of biologically plausible neural networks which simulate the V1 layer of the visual cortex.

Diese Arbeit zeigt ausgehend von einer Darstellung der theoretischen Grundlagen automatischer Textklassifikation, dass die aus der Statistical Learning Theory stammenden Support Vector Machines geeignet sind, zu einer präziseren Erkennung unerwünschter E-Mail-Werbung beizutragen. In einer Testumgebung mit einem Corpus von 20 000 E-Mails wurden Testläufe verschiedene Parameter der Vorverarbeitung und der Support Vector Machine automatisch evaluiert und grafisch visualisiert. Aufbauend darauf wird eine Erweiterung für die Open-Source-Software SpamAssassin beschrieben, die die vorhandenen Klassifikationsmechanismen um eine Klassifikation per Support Vector Machine erweitert.

Dissertation--Ruhr-Universität, Bochum, 2004. / Includes bibliographical references (p. 179-187).

Techn. Universiẗat, Diss., 2002--Darmstadt.

Techn. Universiẗat, Diss., 2002--Darmstadt.

Neurosurgery is a demanding medical discipline that requires a complex interplay of several neuroimaging techniques. This allows structural as well as functional information to be recovered and then visualized to the surgeon. In the case of tumor resections this approach allows more fine-grained differentiation of healthy and pathological tissue which positively influences the postoperative outcome as well as the patient's quality of life. In this work, we will discuss several approaches to establish thermal imaging as a novel neuroimaging technique to primarily visualize neural activity and perfusion state in case of ischaemic stroke. Both applications require novel methods for data-preprocessing, visualization, pattern recognition as well as regression analysis of intraoperative thermal imaging. Online multimodal integration of preoperative and intraoperative data is accomplished by a 2D-3D image registration and image fusion framework with an average accuracy of 2.46 mm. In navigated surgeries, the proposed framework generally provides all necessary tools to project intraoperative 2D imaging data onto preoperative 3D volumetric datasets like 3D MR or CT imaging. Additionally, a fast machine learning framework for the recognition of cortical NaCl rinsings will be discussed throughout this thesis. Hereby, the standardized quantification of tissue perfusion by means of an approximated heating model can be achieved. Classifying the parameters of these models yields a map of connected areas, for which we have shown that these areas correlate with the demarcation caused by an ischaemic stroke segmented in postoperative CT datasets. Finally, a semiparametric regression model has been developed for intraoperative neural activity monitoring of the somatosensory cortex by somatosensory evoked potentials. These results were correlated with neural activity of optical imaging. We found that thermal imaging yields comparable results, yet doesn't share the limitations of optical imaging. In this thesis we would like to emphasize that thermal imaging depicts a novel and valid tool for both intraoperative functional and structural neuroimaging.