p-Laplacian Based Graph Neural Networks

11/14/2021
by   Guoji Fu, et al.
0

Graph neural networks (GNNs) have demonstrated superior performance for semi-supervised node classification on graphs, as a result of their ability to exploit node features and topological information simultaneously. However, most GNNs implicitly assume that the labels of nodes and their neighbors in a graph are the same or consistent, which does not hold in heterophilic graphs, where the labels of linked nodes are likely to differ. Hence, when the topology is non-informative for label prediction, ordinary GNNs may work significantly worse than simply applying multi-layer perceptrons (MLPs) on each node. To tackle the above problem, we propose a new p-Laplacian based GNN model, termed as ^pGNN, whose message passing mechanism is derived from a discrete regularization framework and could be theoretically explained as an approximation of a polynomial graph filter defined on the spectral domain of p-Laplacians. The spectral analysis shows that the new message passing mechanism works simultaneously as low-pass and high-pass filters, thus making ^pGNNs are effective on both homophilic and heterophilic graphs. Empirical studies on real-world and synthetic datasets validate our findings and demonstrate that ^pGNNs significantly outperform several state-of-the-art GNN architectures on heterophilic benchmarks while achieving competitive performance on homophilic benchmarks. Moreover, ^pGNNs can adaptively learn aggregation weights and are robust to noisy edges.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

03/20/2022

LEReg: Empower Graph Neural Networks with Local Energy Regularization

Researches on analyzing graphs with Graph Neural Networks (GNNs) have be...
08/20/2020

Complete the Missing Half: Augmenting Aggregation Filtering with Diversification for Graph Convolutional Networks

The core operation of Graph Neural Networks (GNNs) is the aggregation en...
10/27/2021

VQ-GNN: A Universal Framework to Scale up Graph Neural Networks using Vector Quantization

Most state-of-the-art Graph Neural Networks (GNNs) can be defined as a f...
06/15/2020

Fast Graph Attention Networks Using Effective Resistance Based Graph Sparsification

The attention mechanism has demonstrated superior performance for infere...
06/16/2021

Distilling Self-Knowledge From Contrastive Links to Classify Graph Nodes Without Passing Messages

Nowadays, Graph Neural Networks (GNNs) following the Message Passing par...
12/14/2021

Improving Spectral Graph Convolution for Learning Graph-level Representation

From the original theoretically well-defined spectral graph convolution ...
04/30/2022

Graph Anisotropic Diffusion

Traditional Graph Neural Networks (GNNs) rely on message passing, which ...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.