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

The core operation of current Graph Neural Networks (GNNs) is the aggregation enabled by the graph Laplacian or message passing, which filters the neighborhood node information. Though effective for various tasks, in this paper, we show that they are potentially a problematic factor underlying all GNN methods for learning on certain datasets, as they force the node representations similar, making the nodes gradually lose their identity and become indistinguishable. Hence, we augment the aggregation operations with their dual, i.e. diversification operators that make the node more distinct and preserve the identity. Such augmentation replaces the aggregation with a two-channel filtering process that, in theory, is beneficial for enriching the node representations. In practice, the proposed two-channel filters can be easily patched on existing GNN methods with diverse training strategies, including spectral and spatial (message passing) methods. In the experiments, we observe desired characteristics of the models and significant performance boost upon the baselines on 9 node classification tasks

When Do Graph Neural Networks Help with Node Classification: Investigating the Homophily Principle on Node Distinguishability

Homophily principle, i.e. nodes with the same labels are more likely to be connected, has been believed to be the main reason for the performance superiority of Graph Neural Networks (GNNs) over node-based Neural Networks on Node Classification tasks. Recent research suggests that, even in the absence of homophily, the advantage of GNNs still exists as long as nodes from the same class share similar neighborhood patterns. However, this argument only considers intra-class Node Distinguishability (ND) and neglects inter-class ND, which provides incomplete understanding of homophily. In this paper, we first demonstrate the aforementioned insufficiency with examples and argue that an ideal situation for ND is to have smaller intra-class ND than inter-class ND. To formulate this idea, we propose Contextual Stochastic Block Model for Homophily (CSBM-H) and define two metrics, Probabilistic Bayes Error (PBE) and negative generalized Jeffreys divergence, to quantify ND, through which we can find how intra- and inter-class ND influence ND together. We visualize the results and give detailed analysis. Through experiments, we verified that the superiority of GNNs is indeed closely related to both intra- and inter-class ND regardless of homophily levels, based on which we propose a new performance metric beyond homophily, which is non-linear and feature-based. Experiments indicate it significantly more effective than the existing homophily metrics on revealing the advantage and disadvantage of GNNs on both synthetic and benchmark real-world datasets