On the Spectral Evolution of Large Networks J´er^omeKunegis Institute for Web Science and Technologies University of Koblenz-Landau
[email protected] November 2011 Vom Promotionsausschuss des Fachbereichs 4: Informatik der Universit¨at Koblenz-Landau zur Verleihung des akademischen Grades Doktor der Naturwissenschaften (Dr. rer. nat.) genehmigte Dissertation. PhD thesis at the University of Koblenz-Landau. Datum der wissenschaftlichen Aussprache: 9. November 2011 Vorsitz des Promotionsausschusses: Prof. Dr. Karin Harbusch Berichterstatter: Prof. Dr. Steffen Staab Berichterstatter: Prof. Dr. Christian Bauckhage Berichterstatter: Prof. Dr. Klaus Obermayer Abstract In this thesis, I study 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. The spectral evolution model states that over time, the eigenvalues of a network change while its eigenvectors stay approximately constant. I validate the spectral evolution model empirically on over a hundred network datasets, and theoretically by showing that it generalizes a certain number of known link prediction functions, including graph kernels, path counting methods, rank reduction and triangle closing. The collection of datasets I use contains 118 distinct network datasets. One dataset, the signed social network of the Slashdot Zoo, was specifically extracted during work on this thesis. I also show that the spectral evolution model can be understood as a generalization of the preferential attachment model, if we consider growth in latent dimensions of a network individually. As applications of the spectral evolution model, I introduce two new link prediction algo- rithms that can be used for recommender systems, search engines, collaborative filtering, rating prediction, link sign prediction and more.