Is Heterophily A Real Nightmare For Graph Neural Networks To Do Node Classification?

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.

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Results from the Paper


Task Dataset Model Metric Name Metric Value Global Rank Result Benchmark
Node Classification Actor ACMII-Snowball-2 Accuracy 41.1 ± 0.75 # 5
Node Classification Actor ACMII-GCN Accuracy 41.84 ± 1.15 # 1
Node Classification Actor ACM-GCN Accuracy 41.62 ± 1.15 # 2
Node Classification Actor ACM-Snowball-2 Accuracy 41.4 ± 1.23 # 3
Node Classification Actor ACM-Snowball-3 Accuracy 41.27 ± 0.8 # 4
Node Classification Actor ACMII-Snowball-3 Accuracy 40.31 ± 1.6 # 6
Node Classification Chameleon ACM-Snowball-3 Accuracy 68.38 ± 1.36 # 11
Node Classification Chameleon ACMII-Snowball-2 Accuracy 67.83 ± 2.63 # 12
Node Classification Chameleon ACM-GCN Accuracy 69.04 ± 1.74 # 9
Node Classification Chameleon ACM-Snowball-2 Accuracy 68.51 ± 1.7 # 10
Node Classification Chameleon ACMII-Snowball-3 Accuracy 67.53 ± 2.83 # 13
Node Classification Citeseer ACM-GCN Accuracy 81.68 ± 0.97 # 3
Node Classification Citeseer ACM-Snowball-2 Accuracy 81.58 ± 1.23 # 4
Node Classification Citeseer ACMII-Snowball-3 Accuracy 81.56 ± 1.15 # 5
Node Classification Citeseer ACMII-Snowball-2 Accuracy 82.07 ± 1.04 # 1
Node Classification Citeseer ACM-Snowball-3 Accuracy 81.32 ± 0.97 # 6
Node Classification Citeseer ACMII-GCN Accuracy 81.79 ± 0.95 # 2
Node Classification Cora ACMII-Snowball-3 Accuracy 89.36% ± 1.26% # 4
Node Classification Cora ACM-GCN Accuracy 88.62% ± 1.22% # 7
Node Classification Cora ACM-Snowball-2 Accuracy 88.83% ± 1.49% # 6
Node Classification Cora ACMII-GCN Accuracy 88.95% ± 1.04% # 5
Node Classification Cora ACM-Snowball-3 Accuracy 89.59% ± 1.58% # 2
Node Classification Cornell ACMII-Snowball-2 Accuracy 95.25 ± 1.55 # 2
Node Classification Cornell ACM-Snowball-3 Accuracy 94.26 ± 2.57 # 5
Node Classification Cornell ACM-GCN Accuracy 94.75 ± 2.41 # 4
Node Classification Cornell ACMII-GCN Accuracy 95.9 ± 1.83 # 1
Node Classification Cornell ACM-Snowball-2 Accuracy 95.08 ± 2.07 # 3
Node Classification Cornell ACMII-Snowball-3 Accuracy 93.61 ± 2.79 # 6
Node Classification Pubmed ACM-Snowball-2 Accuracy 90.81 ± 0.52 # 3
Node Classification Pubmed ACM-GCN Accuracy 90.74 ± 0.5 # 4
Node Classification Pubmed ACM-Snowball-3 Accuracy 91.44 ± 0.59 # 1
Node Classification Pubmed ACMII-Snowball-3 Accuracy 91.31 ± 0.6 # 2
Node Classification Pubmed ACMII-Snowball-2 Accuracy 90.56 ± 0.39 # 5
Node Classification Squirrel ACMII-GCN Accuracy 54.53 ± 2.09 # 11
Node Classification Squirrel ACMII-Snowball-2 Accuracy 53.48 ± 0.6 # 12
Node Classification Squirrel ACMII-Snowball-3 Accuracy 52.31 ± 1.57 # 13
Node Classification Squirrel ACM-Snowball-3 Accuracy 55.73 ± 2.39 # 9
Node Classification Squirrel ACM-Snowball-2 Accuracy 55.97 ± 2.03 # 7
Node Classification Squirrel ACM-GCN Accuracy 58.02 ± 1.86 # 4
Node Classification Texas ACM-Snowball-3 Accuracy 94.75 ± 2.41 # 5
Node Classification Texas ACM-Snowball-2 Accuracy 95.74 ± 2.22 # 1
Node Classification Texas ACMII-Snowball-2 Accuracy 95.25 ± 1.55 # 2
Node Classification Texas ACM-GCN Accuracy 94.92 ± 2.88 # 4
Node Classification Texas ACMII-Snowball-3 Accuracy 94.75 ± 3.09 # 5
Node Classification Texas ACMII-GCN Accuracy 95.08 ± 2.07 # 3
Node Classification Wisconsin ACMII-Snowball-3 Accuracy 97.00 ± 2.63 # 1
Node Classification Wisconsin ACM-GCN Accuracy 95.75 ± 2.03 # 4
Node Classification Wisconsin ACM-Snowball-3 Accuracy 96.63 ± 2.24 # 2
Node Classification Wisconsin ACM-Snowball-2 Accuracy 96.38 ± 2.59 # 3

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