Feature Expansion for Graph Neural Networks

TL;DR

This paper investigates the feature space of graph neural networks, revealing linear correlations caused by repeated aggregations, and proposes methods to expand this space for improved learning.

Contribution

It systematically analyzes the feature space of GNNs, introduces techniques for feature space expansion, and demonstrates their effectiveness through extensive experiments.

Findings

Feature space tends to be linearly correlated due to repeated aggregations.

Proposed feature space expansion methods improve learning performance.

Expanded feature space achieves comparable inference time with better convergence.

Abstract

Graph neural networks aim to learn representations for graph-structured data and show impressive performance, particularly in node classification. Recently, many methods have studied the representations of GNNs from the perspective of optimization goals and spectral graph theory. However, the feature space that dominates representation learning has not been systematically studied in graph neural networks. In this paper, we propose to fill this gap by analyzing the feature space of both spatial and spectral models. We decompose graph neural networks into determined feature spaces and trainable weights, providing the convenience of studying the feature space explicitly using matrix space analysis. In particular, we theoretically find that the feature space tends to be linearly correlated due to repeated aggregations. Motivated by these findings, we propose 1) feature subspaces flattening and 2) structural principal components to expand the feature space. Extensive experiments verify the effectiveness of our proposed more comprehensive feature space, with comparable inference time to the baseline, and demonstrate its efficient convergence capability.