Graph Kernels: State-of-the-Art and Future Challenges

Among the data structures commonly used in machine learning, graphs are arguably one of the most general. Graphs allow modelling complex objects as a collection of entities (nodes) and of relationships between such entities (edges), each of which can be annotated by metadata such as categorical or vectorial node and edge features. Many ubiquitous data types can be understood as particular cases of graphs, including unstructured vectorial data as well as structured data types such as time series, images, volumetric data, point clouds or bags of entities, to name a few. Most importantly, numerous applications benefit from the extra flexibility that graph-based representations provide. In chemoinformatics, graphs have been used extensively to represent molecular compounds (Trinajstic, 2018), with nodes corresponding to atoms, edges to chemical bonds, and node and edge features encoding known chemical properties of each atom and bond in the molecule. Machine learning approaches operating on such graph-based representations of molecules are becoming increasingly successful in learning to predict complex molecular properties from large annotated data sets (Duvenaud et al., 2015; Gilmer et al., 2017; Wu et al., 2018), offering a promising set of tools for drug discovery (Vamathevan et al., 2019). In computational biology, graphs have likewise risen to prominence due to their ability to describe multifaceted interactions between (biological) entities.