Predict then Propagate: Graph Neural Networks meet Personalized PageRank

Neural message passing algorithms for semi-supervised classification on graphs have recently achieved great success. However, for classifying a node these methods only consider nodes that are a few propagation steps away and the size of this utilized neighborhood is hard to extend. In this paper, we use the relationship between graph convolutional networks (GCN) and PageRank to derive an improved propagation scheme based on personalized PageRank. We utilize this propagation procedure to construct a simple model, personalized propagation of neural predictions (PPNP), and its fast approximation, APPNP. Our model's training time is on par or faster and its number of parameters on par or lower than previous models. It leverages a large, adjustable neighborhood for classification and can be easily combined with any neural network. We show that this model outperforms several recently proposed methods for semi-supervised classification in the most thorough study done so far for GCN-like models. Our implementation is available online.

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Results from the Paper


Task Dataset Model Metric Name Metric Value Global Rank Uses Extra
Training Data
Result Benchmark
Node Classification Chameleon (60%/20%/20% random splits) APPNP 1:1 Accuracy 51.91 ± 0.56 # 33
Node Classification on Non-Homophilic (Heterophilic) Graphs Chameleon(60%/20%/20% random splits) APPNP 1:1 Accuracy 51.91 ± 0.56 # 29
Node Classification Citeseer PPNP Accuracy 75.83% # 18
Validation YES # 1
Node Classification Citeseer APPNP Accuracy 75.73% # 21
Node Classification CiteSeer (60%/20%/20% random splits) APPNP 1:1 Accuracy 68.59 ± 0.30 # 29
Node Classification Cora APPNP Accuracy 85.09% ± 0.25% # 28
Validation YES # 1
Node Classification Cora PPNP Accuracy 85.29% ± 0.25% # 26
Validation YES # 1
Node Classification Cora (60%/20%/20% random splits) APPNP 1:1 Accuracy 79.41 ± 0.38 # 29
Node Classification on Non-Homophilic (Heterophilic) Graphs Cornell (60%/20%/20% random splits) APPNP 1:1 Accuracy 91.80 ± 0.63 # 16
Node Classification Cornell (60%/20%/20% random splits) APPNP 1:1 Accuracy 91.80 ± 0.63 # 16
Node Classification on Non-Homophilic (Heterophilic) Graphs Deezer-Europe APPNP 1:1 Accuracy 67.21±0.56 # 6
Node Classification Film (60%/20%/20% random splits) APPNP 1:1 Accuracy 38.86 ± 0.24 # 20
Node Classification genius APPNP Accuracy 85.36 ± 0.62 # 16
Node Classification on Non-Homophilic (Heterophilic) Graphs genius APPNP 1:1 Accuracy 85.36 ± 0.62 # 18
Node Classification MS ACADEMIC APPNP Accuracy 93.27 ± 0.08 # 1
Node Classification Penn94 APPNP Accuracy 74.33 ± 0.38 # 21
Node Classification on Non-Homophilic (Heterophilic) Graphs Penn94 APPNP 1:1 Accuracy 74.33 ± 0.38 # 22
Node Classification Pubmed APPNP Accuracy 79.73 ± 0.31 # 38
Validation YES # 1
Node Classification PubMed (60%/20%/20% random splits) APPNP 1:1 Accuracy 85.02 ± 0.09 # 34
Node Classification Squirrel (60%/20%/20% random splits) APPNP 1:1 Accuracy 34.77 ± 0.34 # 33
Node Classification Texas (60%/20%/20% random splits) APPNP 1:1 Accuracy 91.18 ± 0.70 # 18
Node Classification on Non-Homophilic (Heterophilic) Graphs Texas(60%/20%/20% random splits) APPNP 1:1 Accuracy 91.18 ± 0.70 # 17
Node Classification on Non-Homophilic (Heterophilic) Graphs twitch-gamers APPNP 1:1 Accuracy 60.97 ± 0.10 # 22
Node Classification Wisconsin (60%/20%/20% random splits) APPNP 1:1 Accuracy 92.00 ± 3.59 # 17
Node Classification on Non-Homophilic (Heterophilic) Graphs Wisconsin(60%/20%/20% random splits) APPNP 1:1 Accuracy 92.00 ± 3.59 # 17

Methods