Funding: NWO Veni grant (Clara Stegehuis)
Running Period: 2021-2024
Staff: Dr. Clara Stegehuis
Ph.D. student: Riccardo Michielan
ABSTRACT
Networks are everywhere, from social networks to the Internet to the connections in our brain. In many network data, vertices have a large number of features, such as clicks, likes and locations. These features position the vertices in a geometric space, where each coordinate represents one feature. Often, the number of features is staggeringly high, creating a high-dimensional geometry.
Geometric structures explain several key network properties. For example, two of your friends are likely to have similar features to you. Therefore, they have similar features to each other. This makes it likely that they know each other, forming a triangle with you. Thus, geometric structures induce a large number of triangles. Other properties may not be a consequence of the underlying geometry, but a characteristic property of the particular network. These characteristic frequently occurring patterns have important applications, such as spam detection and early identification of financial crises. But which connection patterns are characteristic for a network and which are caused by the underlying geometry?
This project aims to answer this question by studying connection patterns or subgraphs in networks with high-dimensional geometry as well as variability in the number of neighbors. This involves the design of new optimization models and new test statistics.
The second aim of this project is to investigate which network properties are captured by connection patterns. In particular, it focuses on subgraphs in so-called embeddings: simpler network descriptions that have shown great results on tasks such as item recommendation and missing link prediction.