Novel image processing techniques have been in development for decades, but most of these techniques are barely used in real world applications. This results in a gap between image processing research and real-world applications; this thesis aims to close this gap. In an initial study, the quantification, propagation, and communication of uncertainty were determined to be key features in gaining acceptance for new image processing techniques in applications. This thesis presents a holistic approach based on a novel image processing pipeline, capable of quantifying, propagating, and communicating image uncertainty. This work provides an improved image data transformation paradigm, extending image data using a flexible, high-dimensional uncertainty model. Based on this, a completely redesigned image processing pipeline is presented. In this pipeline, each step respects and preserves the underlying image uncertainty, allowing image uncertainty quantification, image pre-processing, image segmentation, and geometry extraction. This is communicated by utilizing meaningful visualization methodologies throughout each computational step. The presented methods are examined qualitatively by comparing to the Stateof- the-Art, in addition to user evaluation in different domains. To show the applicability of the presented approach to real world scenarios, this thesis demonstrates domain-specific problems and the successful implementation of the presented techniques in these domains.

In recent years, enormous progress has been made in the field of Artificial Intelligence (AI). Especially the introduction of Deep Learning and end-to-end learning, the availability of large datasets and the necessary computational power in form of specialised hardware allowed researchers to build systems with previously unseen performance in areas such as computer vision, machine translation and machine gaming. In parallel, the Semantic Web and its Linked Data movement have published many interlinked RDF datasets, forming the world’s largest, decentralised and publicly available knowledge base. Despite these scientific successes, all current systems are still narrow AI systems. Each of them is specialised to a specific task and cannot easily be adapted to all other human intelligence tasks, as would be necessary for Artificial General Intelligence (AGI). Furthermore, most of the currently developed systems are not able to learn by making use of freely available knowledge such as provided by the Semantic Web. Autonomous incorporation of new knowledge is however one of the pre-conditions for human-like problem solving. This work provides a small step towards teaching machines such human-like reasoning on freely available knowledge from the Semantic Web. We investigate how human associations, one of the building blocks of our thinking, can be simulated with Linked Data. The two main results of these investigations are a ground truth dataset of semantic associations and a machine learning algorithm that is able to identify patterns for them in huge knowledge bases. The ground truth dataset of semantic associations consists of DBpedia entities that are known to be strongly associated by humans. The dataset is published as RDF and can be used for future research. The developed machine learning algorithm is an evolutionary algorithm that can learn SPARQL queries from a given SPARQL endpoint based on a given list of exemplary source-target entity pairs. The algorithm operates in an end-to-end learning fashion, extracting features in form of graph patterns without the need for human intervention. The learned patterns form a feature space adapted to the given list of examples and can be used to predict target candidates from the SPARQL endpoint for new source nodes. On our semantic association ground truth dataset, our evolutionary graph pattern learner reaches a Recall@10 of > 63 % and an MRR (& MAP) > 43 %, outperforming all baselines. With an achieved Recall@1 of > 34% it even reaches average human top response prediction performance. We also demonstrate how the graph pattern learner can be applied to other interesting areas without modification.

Computational problems that involve dynamic data, such as physics simulations and program development environments, have been an important subject of study in programming languages. Recent advances in self-adjusting computation made progress towards achieving efficient incremental computation by providing algorithmic language abstractions to express computations that respond automatically to dynamic changes in their inputs. Selfadjusting programs have been shown to be efficient for a broad range of problems via an explicit programming style, where the programmer uses specific primitives to identify, create and operate on data that can change over time. This dissertation presents implicit self-adjusting computation, a type directed technique for translating purely functional programs into self-adjusting programs. In this implicit approach, the programmer annotates the (toplevel) input types of the programs to be translated. Type inference finds all other types, and a type-directed translation rewrites the source program into an explicitly self-adjusting target program. The type system is related to information-flow type systems and enjoys decidable type inference via constraint solving. We prove that the translation outputs well-typed self-adjusting programs and preserves the source program’s input-output behavior, guaranteeing that translated programs respond correctly to all changes to their data. Using a cost semantics, we also prove that the translation preserves the asymptotic complexity of the source program. As a second contribution, we present two techniques to facilitate the processing of large and dynamic data in self-adjusting computation. First, we present a type system for precise dependency tracking that minimizes the time and space for storing dependency metadata. The type system improves the scalability of self-adjusting computation by eliminating an important assumption of prior work that can lead to recording spurious dependencies. We present a type-directed translation algorithm that generates correct selfadjusting programs without relying on this assumption. Second, we show a probabilistic-chunking technique to further decrease space usage by controlling the fundamental space-time tradeoff in self-adjusting computation. We implement implicit self-adjusting computation as an extension to Standard ML with compiler and runtime support. Using the compiler, we are able to incrementalize an interesting set of applications, including standard list and matrix benchmarks, ray tracer, PageRank, sparse graph connectivity, and social circle counts. Our experiments show that our compiler incrementalizes existing code with only trivial amounts of annotation, and the resulting programs bring asymptotic improvements to large datasets from real-world applications, leading to orders of magnitude speedups in practice.

If gradient based derivative algorithms are used to improve industrial products by reducing their target functions, the derivatives need to be exact. The last percent of possible improvement, like the efficiency of a turbine, can only be gained if the derivatives are consistent with the solution process that is used in the simulation software. It is problematic that the development of the simulation software is an ongoing process which leads to the use of approximated derivatives. If a derivative computation is implemented manually, it will be inconsistent after some time if it is not updated. This thesis presents a generalized approach which differentiates the whole simulation software with Algorithmic Differentiation (AD), and guarantees a correct and consistent derivative computation after each change to the software. For this purpose, the variable tagging technique is developed. The technique checks at run-time if all dependencies, which are used by the derivative algorithms, are correct. Since it is also necessary to check the correctness of the implementation, a theorem is developed which describes how AD derivatives can be compared. This theorem is used to develop further methods that can detect and correct errors. All methods are designed such that they can be applied in real world applications and are used within industrial configurations. The process described above yields consistent and correct derivatives but the efficiency can still be improved. This is done by deriving new derivative algorithms. A fixed-point iterator approach, with a consistent derivation, yields all state of the art algorithms and produces two new algorithms. These two new algorithms include all implementation details and therefore they produce consistent derivative results. For detecting hot spots in the application, the state of the art techniques are presented and extended. The data management is changed such that the performance of the software is affected only marginally when quantities, like the number of input and output variables or the memory consumption, are computed for the detection. The hot spots can be treated with techniques like checkpointing or preaccumulation. How these techniques change the time and memory consumption is analyzed and it is shown how they need to be used in selected AD tools. As a last step, the used AD tools are analyzed in more detail. The major implementation strategies for operator overloading AD tools are presented and implementation improvements for existing AD tools are discussed.\ The discussion focuses on a minimal memory consumption and makes it possible to compare AD tools on a theoretical level. The new AD tool CoDiPack is based on these findings and its design and concepts are presented. The improvements and findings in this thesis make it possible, that an automatic, consistent and correct derivative is generated in an efficient way for industrial applications.

The identification of entities that play an important role in a system is one of the fundamental analyses being performed in network studies. This topic is mainly related to centrality indices, which quantify node centrality with respect to several properties in the represented network. The nodes identified in such an analysis are called central nodes. Although centrality indices are very useful for these analyses, there exist several challenges regarding which one fits best for a network. In addition, if the usage of only one index for determining central nodes leads to under- or overestimation of the importance of nodes and is insufficient for finding important nodes, then the question is how multiple indices can be used in conjunction in such an evaluation. Thus, in this thesis an approach is proposed that includes multiple indices of nodes, each indicating an aspect of importance, in the respective evaluation and where all the aspects of a node’s centrality are analyzed in an explorative manner. To achieve this aim, the proposed idea uses fuzzy operators, including a parameter for generating different types of aggregations over multiple indices. In addition, several preprocessing methods for normalization of those values are proposed and discussed. We investigate whether the choice of different decisions regarding the aggregation of the values changes the ranking of the nodes or not. It is revealed that (1) there are nodes that remain stable among the top-ranking nodes, which makes them the most central nodes, and there are nodes that remain stable among the bottom-ranking nodes, which makes them the least central nodes; and (2) there are nodes that show high sensitivity to the choice of normalization methods and/or aggregations. We explain both cases and the reasons why the nodes’ rankings are stable or sensitive to the corresponding choices in various networks, such as social networks, communication networks, and air transportation networks.