Defence of doctoral thesis in the field of mathematics, Msc Joona Karjalainen

Many everyday phenomena can be described with networks. One current example would be networks where the nodes and edges describe contacts or physical proximity of people. Various kinds of network phenomena and data are observed in many fields of science, such as biology, sociology, and computer science.

Network data often shows signs of community structure, i.e., some of the nodes form dense clusters with relatively few connections to the rest of the nodes. This kind of structure may indicate that the nodes share some unobserved property, such as a common hobby or geographical location. Community structures are often studied with models where each node can belong to only one community. However, since the edges of the network may be formed by many different mechanisms, it is natural to allow the communities to overlap.

This dissertation presents probabilistic network models with overlapping communities and studies their structure and statistical properties. The results on the structure of the models suggest that certain empirical observations on real network data, such as clustering properties and power laws, can be explained with unobserved overlapping communities. New estimators are presented for the model parameters, and mathematical proofs are given for their accuracy as the size of the data grows. The presented methods could be used, for example, to assess whether the communities of an observed network are large or small, or dense or sparse.

Opponent is Professor Remco van der Hofstad, Eindhoven university of technology, The Netherlands

Custos is Professor Lasse Leskelä, Aalto University School of Science, Department of Mathematics and Systems Analysis

Contact details of the doctoral student: [email protected], 0407151227

The public defence will be organised on campus and via Zoom.  Link to the event

The doctoral thesis is publicly displayed 10 days before the defence in the publication archive Aaltodoc of Aalto University.

Electronic thesis