Dr. Jérôme Kunegis
- Network Theory and Dynamic Systems (in English), SoSe 2013
- Proseminar "Soziale Netzwerke" (Social Networks), SoSe 2013
- Grundlagen der Datenbanken (Database Systems), WiSe 2012/2013
- Proseminar "Soziale Netzwerke" (Social Networks), SoSe 2012
- Grundlagen der Datenbanken (Database Systems), WiSe 2011/2012
- Grundlagen der Datenbanken (Database Systems), WiSe 2010/2011
- Analysis of large networks
- Spectral graph theory
- Graphs with special structure: signed graphs, directed graphs, weighted graphs and semantic networks
I study the Web using spectral methods. This includes studying individual networks such as Facebook, Twitter, Wikipedia, etc., as well as the Web as a whole in the form of semantic networks. My PhD thesis is about the spectral analysis of individual networks; my post-doctoral work will expand to semantic networks.
My work can be applied on three levels:
- Network characteristics: Connectedness, balance, conflict, clustering, etc.
- Node characteristics: Trust, popularity, centrality, etc.
- Link analysis: link prediction, rating prediction, recommendation, personalized ranking, etc.
The methods I use are spectral, i.e. they are based on characteristic graph matrices such as the adjacency matrix and the Laplacian matrix. I am particularly interested in ways to formulate network mining algorithms algebraically to find connections to other algorithms. In fact, my view is that all link prediction algorithms can be expressed over all paths between two nodes in the network, given suitable operations for aggregating adjacent and parallel edges. These two operations can be reduced to multiplication and addition in a suitable semiring, where link prediction functions can be expressed as a function of the corresponding adjacency matrix. This justifies algebraic graph theory. If additionally the operations form a field, spectral analysis can be used to simplify the computation of link prediction functions, because most of them can be seen as spectral transformations of the adjacency matrix.
To apply spectral methods to the Semantic Web, I am looking for ways to extend algebraic graph theory to arbitrary edge labels. A first step in this direction is to analyse networks with negatively weighted edges, of which the Slashdot Zoo is a prime example. In this case, the real adjacency matrix can be used, and spectral analysis is possible.
In my PhD thesis, I studied the spectral characteristics of large dynamic networks and formulate the spectral evolution model. The spectral evolution model applies to networks that evolve over time, and describes their spectral decompositions such as the eigenvalue and singular value decomposition. My main result is an interpretation of the spectrum and eigenvectors of networks in terms of global and local effects. I show empirically that the spectrum describes a network on the global level, whereas eigenvectors describe a network at the local level, and derive from this several new link prediction methods.
- INFORMATIK, 2013, Publicity Chair.
- Conf. on Web Science (WebSci), 2011, Publicity Chair.
- Special Session on Uncertainty in Network Mining (UNM) at the Int. Conf. on Information Processing and Management of Uncertainty in Knowledge-based Systems (IPMU), 2010, Technical Chair.
Jérôme Kunegis Institute for Web Science and Technologies Universität Koblenz Universitätsstraße 1 56070 Koblenz Germany