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

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 1 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 realworld 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.Preprint. Under review.

Graph Neural Networks for Graphs with Heterophily: A Survey

“…Through adaptive frequency signal learning, FAGCN could achieve expressive performance on different types of graphs with homophily and heterophily. Apart from low-pass and high-pass filters, ACM [Luan et al, 2021] further involves the identity filter, which is the linear combination of low-pass and high-pass filters. In this way, ACM could adaptively exploit beneficial neighbor information from different filter channels for each node; Meanwhile, its identity filter could guarantee less information loss of the input signal.…”

“…Besides, WRGNN [Suresh et al, 2021] imposes different mapping functions on the ego-node embedding and its neighbor aggregated messages, while GGCN [Yan et al, 2021] simplifies the mapping functions to learnable scalar parameters to separately learn ego-neighbor representations. Moreover, ACM [Luan et al, 2021] adopts the identity filter to separate the ego embedding and then conducts the channel-level combination with its neighbor information in the update function.…”

“…However, realworld graphs do not always obey the homophily assumption but show an opposite property, i.e., heterophily that linked nodes have dissimilar features and different class labels. For instance, in online transaction networks, fraudsters are more likely to build connections with customers instead of other fraudsters [Pandit et al, 2007]; in dating networks, most people prefer to date with people of the opposite gender [Zhu et al, 2021]; in molecular networks, protein structures are more likely composed of different types of amino acids that are linked together [Zhu et al, 2020a]. The examples of homophilic and heterophilic graphs are provided in Fig.…”

Finding Global Homophily in Graph Neural Networks When Meeting Heterophily

“…There are also works (Zhu et al, 2020b;Bo et al, 2021;Chien et al, 2020;Yan et al, 2021;Suresh et al, 2021;Pei et al, 2020;Dong et al, 2021;Lim et al, 2021;Yang et al, 2021;Luan et al, 2021;Zhu et al, 2020a;Liu et al, 2021) that extend GNNs to heterophilous graphs. Some methods propose to leverage both low-pass and high-pass convolutional filters in neighborhood aggregation.…”

High-Order Pooling for Graph Neural Networks with Tensor Decomposition

“…Graph neural networks (GNNs) generalize traditional neural network architectures for data in the Euclidean domain to data in non-Euclidean domains [24,38,31]. As graphs are very general and flexible data structures and are ubiquitous in the real world, GNNs are now widely used in a variety of domains and applications such as social network analysis [18], recommender systems [41], graph reasoning [47], and drug discovery [35].…”