Building Multiple Classifier Systems Using Linear Combinations of Reduced Graphs.

Despite great efforts done in research in the last decades, the classification of general graphs, i.e., graphs with unconstrained labeling and structure, remains a challenging task. Due to the inherent relational structure of graphs it is difficult, or even impossible, to apply standard pattern recognition methods to graphs to achieve high recognition accuracies. Common methods to solve the non-trivial problem of graph classification employ graph matching in conjunction with a distance-based classifier or a kernel machine. In the present paper, we address the specific task of graph classification by means of a novel framework that uses information acquired from a broad range of reduced graph subspaces. Our novel approach can be roughly divided into three successive steps. In the first step, differently reduced graphs are created out of the original graphs relying on node centrality measures. In the second step, we compute the graph edit distance between each reduced graph and all the other graphs of the corresponding graph subspace. Finally, we linearly combine the distances in the third step and feed them into a distance-based classifier to obtain the final classification result. On six graph data sets, we empirically confirm that the proposed multiple classifier system directly benefits from the combined distances computed in the various graph subspaces

Dirichlet Densifier Bounds : Densifying Beyond the Spectral Gap Constraint

In this paper, we characterize the universal bounds of our recently reported Dirichlet Densifier. In particular we aim to study the impact of densification on the bounding of intra-class node similarities. To this end we derive a new bound for commute time estimation. This bound does not rely on the spectral gap, but on graph densification (or graph rewiring). Firstly, we explain how our densifier works and we motivate the bound by showing that implicitly constraining the spectral gap through graph densification cannot fully explain the cluster structure in real-world datasets. Then, we pose our hypothesis about densification: a graph densifier can only deal with a moderate degradation of the spectral gap if the inter-cluster commute distances are significantly shrunk. This points to a more detailed bound which explicitly accounts for the shrinking effect of densification. Finally, we formally develop this bound, thus revealing the deeper implications of graph densification in commute time estimation

Sequential and parallel solution-biased search for subgraph algorithms

Funding: This work was supported by the Engineering and Physical Sciences Research Council (grant numbers EP/P026842/1, EP/M508056/1, and EP/N007565).The current state of the art in subgraph isomorphism solving involves using degree as a value-ordering heuristic to direct backtracking search. Such a search makes a heavy commitment to the first branching choice, which is often incorrect. To mitigate this, we introduce and evaluate a new approach, which we call “solution-biased search”. By combining a slightly-random value-ordering heuristic, rapid restarts, and nogood recording, we design an algorithm which instead uses degree to direct the proportion of search effort spent in different subproblems. This increases performance by two orders of magnitude on satisfiable instances, whilst not affecting performance on unsatisfiable instances. This algorithm can also be parallelised in a very simple but effective way: across both satisfiable and unsatisfiable instances, we get a further speedup of over thirty from thirty-six cores, and over one hundred from ten distributed-memory hosts. Finally, we show that solution-biased search is also suitable for optimisation problems, by using it to improve two maximum common induced subgraph algorithms.Postprin

Design pattern detection framework for TOSCA-topologies

Cloud Computing Patterns are Design Patterns especially for cloud applications and provide abstract solution concepts for often reoccurring problems during the implementation of cloud applications. These concepts are mainly used by developers and modelers. To learn about implemented patterns in a completed application, one has to manually analyze the code and the architecture. To improve this time-consuming method, the possibility of automating this process is investigated. This bachelor's thesis proposes an approach for a Design Pattern Detection Framework, to perform an automatic pattern detection. TOSCA, provided by OASIS, is a standardized description for the development of cloud applications. Their architectures can be described by TOSCA topologies, to model components and relationships among each other. The framework, which is developed in the context of this bachelor's thesis, is written in Java and integrated in Winery, a graphical modeling tool for TOSCA topologies, which is a part of the OpenTOSCA ecosystem. The underlying concept of this work follows an approach to detect which Cloud Computing Patterns are used in TOSCA topologies. The concept defines the modeling of Cloud Computing Patterns with TOSCA topologies and how TOSCA topologies are abstracted, to be comparable with pattern topologies. Further, the use of pattern taxonomies is explained to include the interrelations of Cloud Computing Patterns. Basically, patterns and TOSCA topologies are handled as graphs. Consequential, probabilities for possible patterns can be set. For the detection of pattern graphs in a topology graph, an algorithm for subgraph isomorphism is used.Cloud Computing Patterns sind Entwurfsmuster speziell für Cloudanwendungen und stellen abstrakte Lösungskonzepte für häufig auftretende Probleme bei der Implementierung von Cloudanwendungen bereit. Diese Konzepte werden hauptsächlich von Entwicklern und Modellierern benutzt. Um die Umsetzung eines Pattern in einer fertigen Anwendung zu entdecken, muss der Code und die Architektur von Hand analysiert werden. Um diese zeitintensive Methodik zu verbessern, wurde die Möglichkeit der Automatisierung dieses Prozesses untersucht. Diese Bachelorarbeit stellt einen Ansatz für ein Design Pattern Detection Framework dar, um eine automatische Patternerkennung zu ermöglichen. TOSCA ist eine von OASIS standardisierte Beschreibung für die Entwicklung von Cloudanwendungen. Deren Architekturen können mittels TOSCA Topologien beschrieben werden, um Komponenten und deren Beziehungen zueinander, zu modellieren. Das Framework, das im Rahmen dieser Bachelorarbeit entwickelt wird, ist in Java geschrieben und in die Winery, ein Tool zur grafischen Modellierung von TOSCA Topologien und Teil des OpenTOSCA Ecosystems, integriert. Das zugrundeliegende Konzept dieser Arbeit folgt dem Ansatz, automatisiert zu erkennen, welche Cloud Computing Patterns in TOSCA Topologien verwendet werden. Das Konzept definiert die Modellierung dieser Patterns mittels TOSCA Topologien und wie von TOSCA Topologien abstrahiert werden muss, um TOSCA Topologien mit Pattern Topologien vergleichen zu können. Weiter wird die Verwendung von Pattern Taxonomien erklärt, um die Zusammenhänge zwischen den einzelnen Patterns zu berücksichtigen. Daraus folgend können Wahrscheinlichkeiten für mögliche Patterns gesetzt werden. Für die Erkennung von Patterngraphen in einem Topologiegraph, wird ein Subgraphisomorphismus Algorithmus verwendet