One can fairly adopt the ideas of Donald E. Knuth to conclude that process modeling is both a science and an art. Process modeling does have an aesthetic sense. Similar to composing an opera or writing a novel, process modeling is carried out by humans who undergo creative practices when engineering a process model. Therefore, the very same process can be modeled in a myriad number of ways. Once modeled, processes can be analyzed by employing scientific methods. Usually, process models are formalized as directed graphs, with nodes representing tasks and decisions, and directed arcs describing temporal constraints between the nodes. Common process definition languages, such as Business Process Model and Notation (BPMN) and Event-driven Process Chain (EPC) allow process analysts to define models with arbitrary complex topologies. The absence of structural constraints supports creativity and productivity, as there is no need to force ideas into a limited amount of available structural patterns. Nevertheless, it is often preferable that models follow certain structural rules. A well-known structural property of process models is (well-)structuredness. A process model is (well-)structured if and only if every node with multiple outgoing arcs (a split) has a corresponding node with multiple incoming arcs (a join), and vice versa, such that the set of nodes between the split and the join induces a single-entry-single-exit (SESE) region; otherwise the process model is unstructured. The motivations for well-structured process models are manifold: (i) Well-structured process models are easier to layout for visual representation as their formalizations are planar graphs. (ii) Well-structured process models are easier to comprehend by humans. (iii) Well-structured process models tend to have fewer errors than unstructured ones and it is less probable to introduce new errors when modifying a well-structured process model. (iv) Well-structured process models are better suited for analysis with many existing formal techniques applicable only for well-structured process models. (v) Well-structured process models are better suited for efficient execution and optimization, e.g., when discovering independent regions of a process model that can be executed concurrently. Consequently, there are process modeling languages that encourage well-structured modeling, e.g., Business Process Execution Language (BPEL) and ADEPT. However, the well-structured process modeling implies some limitations: (i) There exist processes that cannot be formalized as well-structured process models. (ii) There exist processes that when formalized as well-structured process models require a considerable duplication of modeling constructs. Rather than expecting well-structured modeling from start, we advocate for the absence of structural constraints when modeling. Afterwards, automated methods can suggest, upon request and whenever possible, alternative formalizations that are "better" structured, preferably well-structured. In this thesis, we study the problem of automatically transforming process models into equivalent well-structured models. The developed transformations are performed under a strong notion of behavioral equivalence which preserves concurrency. The findings are implemented in a tool, which is publicly available. / Im Sinne der Ideen von Donald E. Knuth ist die Prozessmodellierung sowohl Wissenschaft als auch Kunst. Prozessmodellierung hat immer auch eine ästhetische Dimension. Wie das Komponieren einer Oper oder das Schreiben eines Romans, so stellt auch die Prozessmodellierung einen kreativen Akt eines Individuums dar. Somit kann ein Prozess auf unterschiedlichste Weise modelliert werden. Prozessmodelle können anschließend mit wissenschaftlichen Methoden untersucht werden. Prozessmodelle liegen im Regelfall als gerichtete Graphen vor. Knoten stellen Aktivitäten und Entscheidungspunkte dar, während gerichtete Kanten die temporalen Abhängigkeiten zwischen den Knoten beschreiben. Gängige Prozessmodellierungssprachen, zum Beispiel die Business Process Model and Notation (BPMN) und Ereignisgesteuerte Prozessketten (EPK), ermöglichen die Erstellung von Modellen mit einer beliebig komplexen Topologie. Es gibt keine strukturellen Einschränkungen, welche die Kreativität oder Produktivität durch eine begrenzte Anzahl von Modellierungsalternativen einschränken würden. Nichtsdestotrotz ist es oft wünschenswert, dass Modelle bestimmte strukturelle Eigenschaften haben. Ein bekanntes strukturelles Merkmal für Prozessmodelle ist Wohlstrukturiertheit. Ein Prozessmodell ist wohlstrukturiert genau dann, wenn jeder Knoten mit mehreren ausgehenden Kanten (ein Split) einen entsprechenden Knoten mit mehreren eingehenden Kanten (einen Join) hat, und umgekehrt, so dass die Knoten welche zwischen dem Split und dem Join liegen eine single-entry-single-exit (SESE) Region bilden. Ist dies nicht der Fall, so ist das Modell unstrukturiert. Wohlstrukturiertheit ist aufgrund einer Vielzahl von Gründen wünschenswert: (i) Wohlstrukturierte Modelle sind einfacher auszurichten, wenn sie visualisiert werden, da sie planaren Graphen entsprechen. (ii) Wohlstrukturierte Modelle zeichnen sich durch eine höhere Verständlichkeit aus. (iii) Wohlstrukturierte Modelle haben oft weniger Fehler als unstrukturierte Modelle. Auch ist die Wahrscheinlichkeit fehlerhafter Änderungen größer, wenn Modelle unstrukturiert sind. (iv) Wohlstrukturierte Modelle eignen sich besser für die formale Analyse, da viele Techniken nur für wohlstrukturierte Modelle anwendbar sind. (v) Wohlstrukturierte Modelle sind eher für die effiziente Ausführung und Optimierung geeignet, z.B. wenn unabhängige Regionen eines Prozesses für die parallele Ausführung identifiziert werden. Folglich gibt es eine Reihe von Prozessmodellierungssprachen, z.B. die Business Process Execution Language (BPEL) und ADEPT, welche den Modellierer anhalten nur wohlstrukturierte Modelle zu erstellen. Solch wohlstrukturiertes Modellieren impliziert jedoch gewisse Einschränkungen: (i) Es gibt Prozesse, welche nicht mittels wohlstrukturierten Prozessmodellen dargestellt werden können. (ii) Es gibt Prozesse, für welche die wohlstrukturierte Modellierung mit einer erheblichen Vervielfältigung von Modellierungs-konstrukten einhergeht. Aus diesem Grund vertritt diese Arbeit den Standpunkt, dass ohne strukturelle Einschränkungen modelliert werden sollte, anstatt Wohlstrukturiertheit von Beginn an zu verlangen. Anschließend können, sofern gewünscht und wo immer es möglich ist, automatische Methoden Modellierungsalternativen vorschlagen, welche "besser" strukturiert sind, im Idealfall sogar wohlstrukturiert. Die vorliegende Arbeit widmet sich dem Problem der automatischen Transformation von Prozessmodellen in verhaltensäquivalente wohlstrukturierte Prozessmodelle. Die vorgestellten Transformationen erhalten ein strenges Verhaltensequivalenzkriterium, welches die Parallelität wahrt. Die Resultate sind in einem frei verfügbaren Forschungsprototyp implementiert worden.

Proximity scaling (i.e., multidimensional scaling and related methods) is a versatile statistical method whose general idea is to reduce the multivariate complexity in a data set by employing suitable proximities between the data points and finding low-dimensional configurations where the fitted distances optimally approximate these proximities. The ultimate goal, however, is often not only to find the optimal configuration but to infer statements about the similarity of objects in the high-dimensional space based on the the similarity in the configuration. Since these two goals are somewhat at odds it can happen that the resulting optimal configuration makes inferring similarities rather difficult. In that case the solution lacks "clusteredness" in the configuration (which we call "c-clusteredness"). We present a version of proximity scaling, coined cluster optimized proximity scaling (COPS), which solves the conundrum by introducing a more clustered appearance into the configuration while adhering to the general idea of multidimensional scaling. In COPS, an arbitrary MDS loss function is parametrized by monotonic transformations and combined with an index that quantifies the c-clusteredness of the solution. This index, the OPTICS cordillera, has intuitively appealing properties with respect to measuring c-clusteredness. This combination of MDS loss and index is called "cluster optimized loss" (coploss) and is minimized to push any configuration towards a more clustered appearance. The effect of the method will be illustrated with various examples: Assessing similarities of countries based on the history of banking crises in the last 200 years, scaling Californian counties with respect to the projected effects of climate change and their social vulnerability, and preprocessing a data set of hand written digits for subsequent classification by nonlinear dimension reduction. (authors' abstract) / Series: Discussion Paper Series / Center for Empirical Research Methods

Proximity scaling (i.e., multidimensional scaling and related methods) is a versatile statistical method whose general idea is to reduce the multivariate complexity in a data set by employing suitable proximities between the data points and finding low-dimensional configurations where the fitted distances optimally approximate these proximities. The ultimate goal, however, is often not only to find the optimal configuration but to infer statements about the similarity of objects in the high-dimensional space based on the the similarity in the configuration. Since these two goals are somewhat at odds it can happen that the resulting optimal configuration makes inferring similarities rather difficult. In that case the solution lacks "clusteredness" in the configuration (which we call "c-clusteredness"). We present a version of proximity scaling, coined cluster optimized proximity scaling (COPS), which solves the conundrum by introducing a more clustered appearance into the configuration while adhering to the general idea of multidimensional scaling. In COPS, an arbitrary MDS loss function is parametrized by monotonic transformations and combined with an index that quantifies the c-clusteredness of the solution. This index, the OPTICS cordillera, has intuitively appealing properties with respect to measuring c-clusteredness. This combination of MDS loss and index is called "cluster optimized loss" (coploss) and is minimized to push any configuration towards a more clustered appearance. The effect of the method will be illustrated with various examples: Assessing similarities of countries based on the history of banking crises in the last 200 years, scaling Californian counties with respect to the projected effects of climate change and their social vulnerability, and preprocessing a data set of hand written digits for subsequent classification by nonlinear dimension reduction. (authors' abstract) / Series: Discussion Paper Series / Center for Empirical Research Methods