Towards Generalizable Graph Contrastive Learning: An Information Theory Perspective

Graph contrastive learning (GCL) emerges as the most representative approach for graph representation learning, which leverages the principle of maximizing mutual information (InfoMax) to learn node representations applied in downstream tasks. To explore better generalization from GCL to downstream tasks, previous methods heuristically define data augmentation or pretext tasks. However, the generalization ability of GCL and its theoretical principle are still less reported. In this paper, we first propose a metric named GCL-GE for GCL generalization ability. Considering the intractability of the metric due to the agnostic downstream task, we theoretically prove a mutual information upper bound for it from an information-theoretic perspective. Guided by the bound, we design a GCL framework named InfoAdv with enhanced generalization ability, which jointly optimizes the generalization metric and InfoMax to strike the right balance between pretext task fitting and the generalization ability on downstream tasks. We empirically validate our theoretical findings on a number of representative benchmarks, and experimental results demonstrate that our model achieves state-of-the-art performance.

Graph Convolutional Networks using Heat Kernel for Semi-supervised Learning

Graph convolutional networks gain remarkable success in semi-supervised learning on graph structured data. The key to graph-based semisupervised learning is capturing the smoothness of labels or features over nodes exerted by graph structure. Previous methods, spectral methods and spatial methods, devote to defining graph convolution as a weighted average over neighboring nodes, and then learn graph convolution kernels to leverage the smoothness to improve the performance of graph-based semi-supervised learning. One open challenge is how to determine appropriate neighborhood that reflects relevant information of smoothness manifested in graph structure. In this paper, we propose GraphHeat, leveraging heat kernel to enhance low-frequency filters and enforce smoothness in the signal variation on the graph. GraphHeat leverages the local structure of target node under heat diffusion to determine its neighboring nodes flexibly, without the constraint of order suffered by previous methods. GraphHeat achieves state-of-the-art results in the task of graph-based semi-supervised classification across three benchmark datasets: Cora, Citeseer and Pubmed.

A Graph Auto-Encoder for Attributed Network Embedding

Attributed network embedding aims to learn low-dimensional node representations from both network structure and node attributes. Existing methods can be categorized into two groups: (1) the first group learns two separated node representations from network structure and node attribute respectively and concatenating them together; (2) the other group obtains node representations by translating node attributes into network structure or vice versa. However, both groups have their drawbacks. The first group neglects the correlation between these two types of information, while the second group assumes strong dependence between network structure and node attributes. In this paper, we address attributed network embedding from a novel perspective, i.e., learning representation of a target node via modeling its attributed local subgraph. To achieve this goal, we propose a novel graph auto-encoder framework, namely GraphAE. For a target node, GraphAE first aggregates the attribute information from its attributed local subgrah, obtaining its low-dimensional representation. Next, GraphAE diffuses its representation to nodes in its local subgraph to reconstruct their attribute information. Our proposed perspective transfroms the problem of learning node representations into the problem of modeling the context information manifested in both network structure and node attributes, thus having high capacity to learn good node representations for attributed network. Extensive experimental results on real-world datasets demonstrate that the proposed framework outperforms the state-of-the-art network approaches at the tasks of link prediction and node classification.