Orometry, Intrinsic Dimensionality and Learning: Novel Insights into Network Data

Today, networks are an integral part of our world. Let it be real-life friendship networks or social connections that are based on social media. In this thesis, we contribute to the understanding of networks by studying networks from three different perspectives. First, we adapt notions and concepts from orometry to metric data and networks to gain novel insights from a local perspective. Specifically, we study measures of local outstandingness and propose concepts to derive small hierarchies from larger networks. These hierarchies are originally designed for the sake of defining dominance relationships between mountain peaks. Our adaption allows to identify outstanding entities on a local level and small hierarchies between them. Second, we evaluate networks from a global perspective by computing the intrinsic dimensionality of whole networks. Here, a low intrinsic dimensionality stands for data with highly distinguishable data points, which is crucial for learning. To accomplish this, we develop practical algorithms and speed-up techniques to transfer an axiomatically grounded framework to large-scale graph data. Furthermore, as an application, we present a feature selection method based on the developed method for computing intrinsic dimensions. Third, we propose two novel deep learning methods for representation learning on networks, leading to condensed perspectives on them. The first method learns embeddings with the help of techniques from formal concept analysis. This approach leads to a novel paradigm for embedding learning for bipartite graphs as it does not incorporate simple neighborhood information but the concept lattice structure of the corresponding formal context. The second method is a combination of a graph neural network and a language model and is tailored for a special network structure and the special task of author verification. This task deals with the verification of links between authors and publications. Our method is designed such that it can process raw texts and also incorporates past co-authorship edges. In conclusion, this thesis contributes to the understanding and investigation of networks from a local, global, and condensed perspective. This is done by proposing novel measures and structures for them based on orometric concepts and intrinsic dimensionality and by providing novel learning methods for bipartite networks in general and author-publication networks in specific.