The Multiscale Laplacian Graph Kernel

TL;DR

The paper introduces the Multiscale Laplacian Graph kernel (MLG), a novel method for capturing multi-scale structures in graphs by recursively applying a new vertex-based kernel, with a randomized projection for efficiency.

Contribution

It proposes the MLG kernel that models multi-scale graph structures and introduces the FLG kernel to lift vertex kernels to graph kernels, along with a randomized projection for scalability.

Findings

MLG kernel effectively captures multi-scale graph features.

The randomized projection improves computational efficiency.

Experimental results demonstrate superior performance over existing methods.

Abstract

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 Nystr\"om method, but for RKHS operators.