SWING: Unlocking Implicit Graph Representations for Graph Random Features

TL;DR

SWING introduces a novel algorithm for efficiently computing graph random features on implicit graphs using continuous space walks, Fourier analysis, and importance sampling, without explicit graph materialization.

Contribution

It presents SWING, a new method leveraging continuous space walks and Fourier analysis for implicit graph computations, enhancing efficiency and scalability.

Findings

SWING accurately approximates combinatorial calculations on implicit graphs.

The method is accelerator-friendly and does not need explicit graph materialization.

Experiments demonstrate SWING's effectiveness across various implicit graph classes.

Abstract

We propose SWING: Space Walks for Implicit Network Graphs, a new class of algorithms for computations involving Graph Random Features on graphs given by implicit representations (i-graphs), where edge-weights are defined as bi-variate functions of feature vectors in the corresponding nodes. Those classes of graphs include several prominent examples, such as: $\epsilon$-neighborhood graphs, used on regular basis in machine learning. Rather than conducting walks on graphs' nodes, those methods rely on walks in continuous spaces, in which those graphs are embedded. To accurately and efficiently approximate original combinatorial calculations, SWING applies customized Gumbel-softmax sampling mechanism with linearized kernels, obtained via random features coupled with importance sampling techniques. This algorithm is of its own interest. SWING relies on the deep connection between implicitly defined graphs and Fourier analysis, presented in this paper. SWING is accelerator-friendly and does not require input graph materialization. We provide detailed analysis of SWING and complement it with thorough experiments on different classes of i-graphs.