Graph kernel

In structure mining, a graph kernel is a kernel function that computes an inner product on graphs.^[1] Graph kernels can be intuitively understood as functions measuring the similarity of pairs of graphs. They allow kernelized learning algorithms such as support vector machines to work directly on graphs, without having to do feature extraction to transform them to fixed-length, real-valued feature vectors. They find applications in bioinformatics, in chemoinformatics (as a type of molecule kernels^[2]), and in social network analysis.^[1]

Concepts of graph kernels have been around since the 1999, when D. Haussler^[3] introduced convolutional kernels on discrete structures. The term graph kernels was more officially coined in 2002 by R. I. Kondor and J. Lafferty^[4] as kernels on graphs, i.e. similarity functions between the nodes of a single graph, with the World Wide Web hyperlink graph as a suggested application. In 2003, Gärtner et al.^[5] and Kashima et al.^[6] defined kernels between graphs. In 2010, Vishwanathan et al. gave their unified framework.^[1] In 2018, Ghosh et al. ^[7] described the history of graph kernels and their evolution over two decades.