The Multiscale Laplacian Graph Kernel
This provides a method for graph comparison in domains like molecular analysis, addressing a known limitation of existing kernels, but it is incremental as it builds on prior kernel techniques.
The paper tackles the problem of comparing graphs with multiscale structure by introducing the Multiscale Laplacian Graph kernel, which accounts for structure at different scales through a hierarchy of nested subgraphs, achieving computational feasibility via a randomized projection method.
Many real world graphs, such as the graphs of molecules, exhibit structure at multiple different scales, but most existing kernels between graphs are either purely local or purely global in character. In contrast, by building a hierarchy of nested subgraphs, the Multiscale Laplacian Graph kernels (MLG kernels) that we define in this paper can account for structure at a range of different scales. At the heart of the MLG construction is another new graph kernel, called the Feature Space Laplacian Graph kernel (FLG kernel), which has the property that it can lift a base kernel defined on the vertices of two graphs to a kernel between the graphs. The MLG kernel applies such FLG kernels to subgraphs recursively. To make the MLG kernel computationally feasible, we also introduce a randomized projection procedure, similar to the Nyström method, but for RKHS operators.