Learning with Geometric Embeddings of Graphs

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