Graph Kernels via Functional Embedding

TL;DR

This paper introduces a novel graph representation as a functional object derived from adjacency matrix power iteration, leading to an efficient, invariant, and scalable graph kernel that outperforms existing methods on standard benchmarks.

Contribution

The paper presents a new functional embedding for graphs that is invariant under vertex reordering and offers a scalable, efficient kernel with superior classification performance.

Findings

Outperforms state-of-the-art graph kernels on 3 out of 4 benchmarks.

Runs in linear time relative to the number of edges.

Provides a scalable and invariant graph representation.

Abstract

We propose a representation of graph as a functional object derived from the power iteration of the underlying adjacency matrix. The proposed functional representation is a graph invariant, i.e., the functional remains unchanged under any reordering of the vertices. This property eliminates the difficulty of handling exponentially many isomorphic forms. Bhattacharyya kernel constructed between these functionals significantly outperforms the state-of-the-art graph kernels on 3 out of the 4 standard benchmark graph classification datasets, demonstrating the superiority of our approach. The proposed methodology is simple and runs in time linear in the number of edges, which makes our kernel more efficient and scalable compared to many widely adopted graph kernels with running time cubic in the number of vertices.