Global geometric graph kernels and applications
This thesis explores the topics of graph kernels and classification of graphs. Graph kernels have received considerable attention in the last decade, in part because of their value in many practical applications, such as chemo informatics and molecular biology, in which classification using graph kernels have become the standard model for several problems. Perhaps even more important is the inclusion of graph kernels in the rich field of kernel methods, making a large family of machine learning algorithms, including support vector machines, applicable to data naturally represented as graphs. Graph kernels are similarity functions defined on pairs of graphs. Traditionally, graph kernels compare graphs in terms of features of subgraphs such as walks, paths or tree patterns. For the kernels to remain computationally efficient, these subgraphs are often chosen to be small. Because of this fact, most graph kernels adopt an inherently local perspective on the graph and may fail to discern global properties, such as the girth or the chromatic number, that are not captured in local structure. Furthermore, existing work on graph kernels lack results justifying a particular choice of kernel for a given application. In this thesis we propose two new graph kernels, designed to capture global properties of graphs, as described above. At the core of these kernels is Lov ́asz number, an important concept in graph theory with strong connections to graph properties like the chromatic number and the size of the largest clique. We give efficient sampling approximations to both kernels, allowing them to scale to large graphs. We also show that we can characterize the separation margin induced by these kernels in certain classification tasks. This serves as initial progress towards making theory aid kernel choice. We make an extensive empirical evaluation of both kernels on synthetic data with known global properties, and on real graphs frequently used to benchmark graph kernels. Finally, we present a new application of graph kernels in the field of data mining by redefining an important subproblem of entity disambiguation as a graph classification problem. We show empirically that our proposed method improves on the state-of-the-art.