[Paper Review] Is Heterophily A Real Nightmare For Graph Neural Networks To Do Node Classification?

Sitao Luan, Chenqing Hua+6 more|arXiv (Cornell University)|Sep 12, 2021

Advanced Graph Neural NetworksComputer Science40 references44 citations

TL;DR

The paper argues that heterophily is not always harmful for GNNs, introduces a similarity-based aggregation metric and a diversification operation, and presents Adaptive Channel Mixing (ACM) to leverage both low- and high-frequency graph information, achieving strong gains on real-world node classification tasks.

ABSTRACT

Graph Neural Networks (GNNs) extend basic Neural Networks (NNs) by using the graph structures based on the relational inductive bias (homophily assumption). Though GNNs are believed to outperform NNs in real-world tasks, performance advantages of GNNs over graph-agnostic NNs seem not generally satisfactory. Heterophily has been considered as a main cause and numerous works have been put forward to address it. In this paper, we first show that not all cases of heterophily are harmful for GNNs with aggregation operation. Then, we propose new metrics based on a similarity matrix which considers the influence of both graph structure and input features on GNNs. The metrics demonstrate advantages over the commonly used homophily metrics by tests on synthetic graphs. From the metrics and the observations, we find some cases of harmful heterophily can be addressed by diversification operation. With this fact and knowledge of filterbanks, we propose the Adaptive Channel Mixing (ACM) framework to adaptively exploit aggregation, diversification and identity channels in each GNN layer to address harmful heterophily. We validate the ACM-augmented baselines with 10 real-world node classification tasks. They consistently achieve significant performance gain and exceed the state-of-the-art GNNs on most of the tasks without incurring significant computational burden.

Motivation & Objective

• Question the blanket assumption that heterophily always harms GNNs and identify cases where aggregation remains effective.
• Develop new metrics that capture how graph structure and node features influence GNN outputs via a similarity matrix.
• Demonstrate that diversification (high-pass) channels can help address harmful heterophily in conjunction with aggregation.
• Propose and validate the Adaptive Channel Mixing (ACM) framework to adaptively combine LP, HP, and identity channels per node.
• Show empirical gains of ACM-augmented baselines on 10 real-world node classification tasks.

Proposed method

• Construct a backpropagation-based similarity matrix S(Â,X) = (ÂX)(ÂX)ᵀ to measure how aggregation interacts with node features.
• Define Aggregation Similarity metrics Sagg and a modified version Sagg^M to quantify how much aggregation preserves class-consistency after applying Â.
• Introduce Hagg and Hagg^M as aggregation-focused homophily metrics that incorporate the effect of the aggregation operator.
• Demonstrate that Hagg^M is a better predictor of GNN performance than traditional edge/node/class homophily metrics on synthetic graphs.
• Develop Diversification Distinguishability DD to identify nodes that can benefit from high-pass (diversification) filtering.
• Propose a 2-channel/3-channel filterbank interpretation where LP corresponds to aggregation, HP to diversification, and Identity to a direct path, enabling perfect reconstruction when combined.
• Formulate Adaptive Channel Mixing (ACM/ACMII) to learn per-node channel weights and combine LP, HP, and Identity channels in each GNN layer.
• Provide complexity estimates showing ACM doubles running time roughly, with detailed ablations and comparisons on real data.
• Validate ACM-augmented models on 10 real-world node classification datasets, showing consistent gains over baselines.

Experimental results

Research questions

• RQ1 When does graph aggregation harm or help node distinguishability under heterophily?
• RQ2 Can a similarity-based aggregation metric better predict GNN performance than traditional homophily measures?
• RQ3 To what extent can diversification (high-pass filtering) address harmful heterophily in practice?
• RQ4 Does an adaptive channel mixing strategy that jointly utilizes aggregation, diversification, and identity channels improve node classification across heterogeneous graphs?

Key findings

• Aggregation-based GNNs are not universally harmed by heterophily; some heterophilous graphs remain distinguishable after aggregation.
• A similarity-based aggregation metric (Sagg and Hagg) that accounts for both graph structure and node features better explains GNN performance than traditional homophily metrics on synthetic data.
• Diversification (high-pass) can address certain harmful heterophily cases by exploiting neighborhood differences, supporting a filterbank view of graph signals.
• The Adaptive Channel Mixing (ACM/ACMII) framework effectively combines LP, HP, and Identity channels with node-conditioned weights, yielding significant improvements on 10 real-world datasets.
• ACM-augmented baselines consistently outperform state-of-the-art GNNs on most tasks without excessive computational burden, albeit with roughly double per-epoch time compared to baselines.
• Ablation studies confirm contributions from HP and Identity channels and the adaptive mixing mechanism across multiple datasets.