Enhancing the Influence of Labels on Unlabeled Nodes in Graph Convolutional Networks

TL;DR

This work tackles the challenge that label information propagated through GCNs does not always positively impact predictions for unlabeled nodes. It introduces ELU-GCN, a two-stage framework that first learns an ELU-graph to enhance the positive influence of labeled nodes, and then applies a graph-contrastive objective to fuse information from the ELU-graph with the original graph. The approach is backed by theoretical results linking ELU-graph learning to improved generalization and by extensive experiments showing strong performance, especially on heterophilic graphs and unlabeled nodes that previously benefited little from labels. The method achieves a favorable balance between accuracy and running time while providing interpretable ELU-graphs that emphasize same-class connections. This advances label utilization in GCNs with a principled, verifiable framework.

Abstract

The message-passing mechanism of graph convolutional networks (i.e., GCNs) enables label information to reach more unlabeled neighbors, thereby increasing the utilization of labels. However, the additional label information does not always contribute positively to the GCN. To address this issue, we propose a new two-step framework called ELU-GCN. In the first stage, ELU-GCN conducts graph learning to learn a new graph structure (i.e., ELU-graph), which allows the additional label information to positively influence the predictions of GCN. In the second stage, we design a new graph contrastive learning on the GCN framework for representation learning by exploring the consistency and mutually exclusive information between the learned ELU graph and the original graph. Moreover, we theoretically demonstrate that the proposed method can ensure the generalization ability of GCNs. Extensive experiments validate the superiority of our method.

Figures (7)

• Figure 1: An illustration of effective label utilization. Sub-figure (a) wants to assign the label information to node $a$ (gray node) by one unlabeled node (gray node) and two labeled nodes with different classes, i.e., one blue node and one orange node. Moreover, the LPA algorithm is employed to obtain the probability of each labeled node to the node $a$, where the blue node has more influence (or higher probability) than the orange node based on the histogram in the upper right of the sub-figure (a). If the GCN predicts the node $a$ as the orange color (as shown in sub-figure (b)), which is inconsistent with the class with most label information ( i.e., blue). It indicates that the label information provided by the message passing of the GCN does not help classify the node $a$, and may even hinder its correct classification. On the contrary, if GCN predicts the node $a$ as the blue color, i.e., sub-figure (c), it implies that the label information provided by the message passing of the GCN helps to classify the node $a$.
• Figure 2: Visualization of both ELU nodes and NELU nodes in three real datasets, i.e., Cora, Citerseer, and Pubmed. (a) every dataset contains NELU nodes and (b) the classification comparison between ELU nodes and NELU nodes, where ELU nodes have higher classification ability than NELU nodes.
• Figure 3: Visualization of the adjacency matrix of the ELU graph on Cora, Computers, Photo, and Chameleon datasets. The rows and columns are nodes that are reordered based on node labels, the lighter a pixel, the larger the value of the ELU graph matrix weight.
• Figure 4: Scatter plot showing the relationship between model runtime and accuracy, where the x-axis represents the runtime of different models on different datasets and the y-axis represents their corresponding accuracy (%).
• Figure 5: The classification performance of the proposed method at different parameter settings ( i.e., $\tau$, $\lambda$) on the Cora and Citeseer datasets.

Theorems & Definitions (10)

• Proposition 3.1
• Definition 3.2
• Theorem 3.3
• Theorem 3.4
• proof
• Lemma 2.1
• Theorem 2.2
• proof
• Theorem 2.3
• proof