6 research outputs found
\{kappa}HGCN: Tree-likeness Modeling via Continuous and Discrete Curvature Learning
The prevalence of tree-like structures, encompassing hierarchical structures
and power law distributions, exists extensively in real-world applications,
including recommendation systems, ecosystems, financial networks, social
networks, etc. Recently, the exploitation of hyperbolic space for tree-likeness
modeling has garnered considerable attention owing to its exponential growth
volume. Compared to the flat Euclidean space, the curved hyperbolic space
provides a more amenable and embeddable room, especially for datasets
exhibiting implicit tree-like architectures. However, the intricate nature of
real-world tree-like data presents a considerable challenge, as it frequently
displays a heterogeneous composition of tree-like, flat, and circular regions.
The direct embedding of such heterogeneous structures into a homogeneous
embedding space (i.e., hyperbolic space) inevitably leads to heavy distortions.
To mitigate the aforementioned shortage, this study endeavors to explore the
curvature between discrete structure and continuous learning space, aiming at
encoding the message conveyed by the network topology in the learning process,
thereby improving tree-likeness modeling. To the end, a curvature-aware
hyperbolic graph convolutional neural network, \{kappa}HGCN, is proposed, which
utilizes the curvature to guide message passing and improve long-range
propagation. Extensive experiments on node classification and link prediction
tasks verify the superiority of the proposal as it consistently outperforms
various competitive models by a large margin.Comment: KDD 202
Beyond Flatland : exploring graphs in many dimensions
Societies, technologies, economies, ecosystems, organisms, . . . Our world is composed of complex networks—systems with many elements that interact in nontrivial ways. Graphs are natural models of these systems, and scientists have made tremendous progress in developing tools for their analysis. However, research has long focused on relatively simple graph representations and problem specifications, often discarding valuable real-world information in the process. In recent years, the limitations of this approach have become increasingly apparent, but we are just starting to comprehend how more intricate data representations and problem formulations might benefit our understanding of relational phenomena. Against this background, our thesis sets out to explore graphs in five dimensions: descriptivity, multiplicity, complexity, expressivity, and responsibility. Leveraging tools from graph theory, information theory, probability theory, geometry, and topology, we develop methods to (1) descriptively compare individual graphs, (2) characterize similarities and differences between groups of multiple graphs, (3) critically assess the complexity of relational data representations and their associated scientific culture, (4) extract expressive features from and for hypergraphs, and (5) responsibly mitigate the risks induced by graph-structured content recommendations. Thus, our thesis is naturally situated at the intersection of graph mining, graph learning, and network analysis.Gesellschaften, Technologien, Volkswirtschaften, Ökosysteme, Organismen, . . . Unsere Welt besteht aus komplexen Netzwerken—Systemen mit vielen Elementen, die auf nichttriviale Weise interagieren. Graphen sind natürliche Modelle dieser Systeme, und die Wissenschaft hat bei der Entwicklung von Methoden zu ihrer Analyse große Fortschritte gemacht. Allerdings hat sich die Forschung lange auf relativ einfache Graphrepräsentationen und Problemspezifikationen beschränkt, oft unter Vernachlässigung wertvoller Informationen aus der realen Welt. In den vergangenen Jahren sind die Grenzen dieser Herangehensweise zunehmend deutlich geworden, aber wir beginnen gerade erst zu erfassen, wie unser Verständnis relationaler Phänomene von intrikateren Datenrepräsentationen und Problemstellungen profitieren kann. Vor diesem Hintergrund erkundet unsere Dissertation Graphen in fünf Dimensionen: Deskriptivität, Multiplizität, Komplexität, Expressivität, und Verantwortung. Mithilfe von Graphentheorie, Informationstheorie, Wahrscheinlichkeitstheorie, Geometrie und Topologie entwickeln wir Methoden, welche (1) einzelne Graphen deskriptiv vergleichen, (2) Gemeinsamkeiten und Unterschiede zwischen Gruppen multipler Graphen charakterisieren, (3) die Komplexität relationaler Datenrepräsentationen und der mit ihnen verbundenen Wissenschaftskultur kritisch beleuchten, (4) expressive Merkmale von und für Hypergraphen extrahieren, und (5) verantwortungsvoll den Risiken begegnen, welche die Graphstruktur von Inhaltsempfehlungen mit sich bringt. Damit liegt unsere Dissertation naturgemäß an der Schnittstelle zwischen Graph Mining, Graph Learning und Netzwerkanalyse
A Survey on Centrality Metrics and Their Implications in Network Resilience
Centrality metrics have been used in various networks, such as communication,
social, biological, geographic, or contact networks. In particular, they have
been used in order to study and analyze targeted attack behaviors and
investigated their effect on network resilience. Although a rich volume of
centrality metrics has been developed for decades, a limited set of centrality
metrics have been commonly in use. This paper aims to introduce various
existing centrality metrics and discuss their applicabilities and performance
based on the results obtained from extensive simulation experiments to
encourage their use in solving various computing and engineering problems in
networks.Comment: Main paper: 36 pages, 2 figures. Appendix 23 pages,45 figure