Neighborhood Homophily-based Graph Convolutional Network

TL;DR

This paper introduces a new metric called Neighborhood Homophily (NH) to better characterize node neighborhood label purity and integrates it into a GCN framework, NHGCN, to improve classification on diverse graph types.

Contribution

The paper proposes a novel NH metric for measuring neighborhood label purity and incorporates it into GCNs, enabling adaptive neighbor grouping and aggregation for improved performance.

Findings

NHGCN outperforms state-of-the-art methods on various benchmarks.

The NH metric effectively captures neighborhood label complexity.

Adaptive aggregation based on NH improves classification accuracy.

Abstract

Graph neural networks (GNNs) have been proved powerful in graph-oriented tasks. However, many real-world graphs are heterophilous, challenging the homophily assumption of classical GNNs. To solve the universality problem, many studies deepen networks or concatenate intermediate representations, which does not inherently change neighbor aggregation and introduces noise. Recent studies propose new metrics to characterize the homophily, but rarely consider the correlation of the proposed metrics and models. In this paper, we first design a new metric, Neighborhood Homophily (\textit{NH}), to measure the label complexity or purity in node neighborhoods. Furthermore, we incorporate the metric into the classical graph convolutional network (GCN) architecture and propose \textbf{N}eighborhood \textbf{H}omophily-based \textbf{G}raph \textbf{C}onvolutional \textbf{N}etwork (\textbf{NHGCN}). In this framework, neighbors are grouped by estimated \textit{NH} values and aggregated from different channels, and the resulting node predictions are then used in turn to estimate and update \textit{NH} values. The two processes of metric estimation and model inference are alternately optimized to achieve better node classification. NHGCN achieves top overall performance on both homophilous and heterophilous benchmarks, with an improvement of up to 7.4\% compared to the current SOTA methods.