Random Wavelet Features for Graph Kernel Machines

TL;DR

This paper introduces randomized spectral node embeddings that efficiently approximate graph kernels, enabling scalable and accurate graph representation learning, especially for spectrally localized kernels.

Contribution

It proposes a novel randomized spectral approach for node embeddings that better approximates graph kernels compared to existing methods.

Findings

Embeddings achieve more accurate kernel approximations.

Method is effective for spectrally localized kernels.

Embeddings are scalable for large networks.

Abstract

Node embeddings map graph vertices into low-dimensional Euclidean spaces while preserving structural information. They are central to tasks such as node classification, link prediction, and signal reconstruction. A key goal is to design node embeddings whose dot products capture meaningful notions of node similarity induced by the graph. Graph kernels offer a principled way to define such similarities, but their direct computation is often prohibitive for large networks. Inspired by random feature methods for kernel approximation in Euclidean spaces, we introduce randomized spectral node embeddings whose dot products estimate a low-rank approximation of any specific graph kernel. We provide theoretical and empirical results showing that our embeddings achieve more accurate kernel approximations than existing methods, particularly for spectrally localized kernels. These results demonstrate the effectiveness of randomized spectral constructions for scalable and principled graph representation learning.