Learning with Geometric Embeddings of Graphs
Doctoral thesis, 2016

Graphs are natural representations of problems and data in many fields. For example, in computational biology, interaction networks model the functional relationships between genes in living organisms; in the social sciences, graphs are used to represent friendships and business relations among people; in chemoinformatics, graphs represent atoms and molecular bonds. Fields like these are often rich in data, to the extent that manual analysis is not feasible and machine learning algorithms are necessary to exploit the wealth of available information. Unfortunately, in machine learning research, there is a huge bias in favor of algorithms operating only on continuous vector valued data, algorithms that are not suitable for the combinatorial structure of graphs. In this thesis, we show how to leverage both the expressive power of graphs and the strength of established machine learning tools by introducing methods that combine geometric embeddings of graphs with standard learning algorithms. We demonstrate the generality of this idea by developing embedding algorithms for both simple and weighted graphs and applying them in both supervised and unsupervised learning problems such as classification and clustering. Our results provide both theoretical support for the usefulness of graph embeddings in machine learning and empirical evidence showing that this framework is often more flexible and better performing than competing machine learning algorithms for graphs.

EF, Hörsalsvägen 11, Chalmers
Opponent: Prof. Kurt Mehlhorn, Max Planck Institute for Informatics, Saarbrücken, Germany

Author

Fredrik Johansson

Chalmers, Computer Science and Engineering (Chalmers), Computing Science (Chalmers)

Weighted theta functions and embeddings with applications to Max-Cut, clustering and summarization

29th Annual Conference on Neural Information Processing Systems, NIPS 2015, Montreal, Canada, 7-12 December,; Vol. 2015-January(2015)p. 1018-1026

Conference contribution

Entity disambiguation in anonymized graphs using graph kernels

22nd ACM International Conference on Information and Knowledge Management, CIKM 2013; San Francisco, CA; United States; 27 October 2013 through 1 November 2013,; (2013)p. 1037-1046

Paper in proceedings

Global graph kernels using geometric embeddings

Proceedings of the 31st International Conference on Machine Learning, ICML 2014, Beijing, China, 21-26 June 2014,; (2014)p. 694-702

Paper in proceedings

Learning with similarity functions on graphs using matchings of geometric embeddings

Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining,; Vol. 2015-August(2015)p. 467-476

Paper in proceedings

Subject Categories

Probability Theory and Statistics

Computer Science

Discrete Mathematics

ISBN

978-91-7597-491-0

Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 4172

Publisher

Chalmers University of Technology

EF, Hörsalsvägen 11, Chalmers

Opponent: Prof. Kurt Mehlhorn, Max Planck Institute for Informatics, Saarbrücken, Germany

More information

Created

11/18/2016