KONG: Kernels for ordered-neighborhood graphs

TL;DR

This paper introduces novel graph kernels tailored for graphs with ordered neighborhoods, enabling scalable, accurate comparison of such graphs and improving feature informativeness for evolving graph data.

Contribution

It presents new scalable kernels for ordered-neighborhood graphs, combining convolutional and string kernels with sketching techniques, and provides bounds on their accuracy and complexity.

Findings

Ordered neighborhoods lead to more informative features.

The kernels are scalable and efficient for real datasets.

They outperform existing methods in capturing graph similarities.

Abstract

We present novel graph kernels for graphs with node and edge labels that have ordered neighborhoods, i.e. when neighbor nodes follow an order. Graphs with ordered neighborhoods are a natural data representation for evolving graphs where edges are created over time, which induces an order. Combining convolutional subgraph kernels and string kernels, we design new scalable algorithms for generation of explicit graph feature maps using sketching techniques. We obtain precise bounds for the approximation accuracy and computational complexity of the proposed approaches and demonstrate their applicability on real datasets. In particular, our experiments demonstrate that neighborhood ordering results in more informative features. For the special case of general graphs, i.e. graphs without ordered neighborhoods, the new graph kernels yield efficient and simple algorithms for the comparison of label distributions between graphs.