Line Graph Contrastive Learning for Link Prediction

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Highlights

Zehua Zhang, Shilin Sun, Guixiang Ma, Caiming Zhong

•We design a novel contrastive learning framework based on line graph

to be suitable for link prediction on sparse and dense graphs.

•We propose a cross-scale contrastive learning strategy to maximize the

mutual information between subgraph and line graph.

•The dual perspectives contrastive progress to some extent avoids the

problem of inconsistent prediction on the similarity based methods with

single view.

•Our comprehensive experiments on six datasets from diverse areas

demonstrate that our model has better performance on generalization

and robustness than the SOTA methods.

arXiv:2210.13795v2 [cs.LG] 8 Mar 2023

Line Graph Contrastive Learning for Link Prediction

Zehua Zhanga,∗, Shilin Suna,∗∗, Guixiang Mab, Caiming Zhongc

aCollege of Information and Computer,Taiyuan University of Technology,Yuci District,

Jinzhong, 030600, Shanxi, China

bIntel Labs, Hillsboro, Oregon, 97229,USA

cCollege of Science and Technology, Ning bo University,Cixi, Ningbo, 315300, Zhejiang,

China

Abstract

Link prediction tasks focus on predicting possible future connections. Most

existing researches measure the likelihood of links by diﬀerent similarity

scores on node pairs and predict links between nodes. However, the similarity-

based approaches have some challenges in information loss on nodes and

generalization ability on similarity indexes. To address the above issues, we

propose a Line Graph Contrastive Learning(LGCL) method to obtain rich

information with multiple perspectives. LGCL obtains a subgraph view by

h-hop subgraph sampling with target node pairs. After transforming the

sampled subgraph into a line graph, the link prediction task is converted

into a node classiﬁcation task, which graph convolution progress can learn

edge embeddings from graphs more eﬀectively. Then we design a novel cross-

scale contrastive learning framework on the line graph and the subgraph to

maximize the mutual information of them, so that fuses the structure and

∗Co-ﬁrst authors and Corresponding author

∗∗ Co-ﬁrst authors

Email addresses: zhangzehua@tyut.edu.cn (Zehua Zhang), shilin_sun01@163.com

(Shilin Sun), guixiang.ma@intel.com (Guixiang Ma), zhongcaiming@nbu.edu.cn

(Caiming Zhong)

Preprint submitted to Pattern Recognition March 9, 2023

feature information. The experimental results demonstrate that the proposed

LGCL outperforms the state-of-the-art methods and has better performance

on generalization and robustness.

Keywords:

Line Graph, Contrastive Learning, Link Prediction, Node Classiﬁcation,

Mutual Information

1. Introduction

Link prediction task is based on the topological deﬁnition of the network

to predict the existence of links between nodes. It has been applied to various

ﬁelds, such as product recommendations [1], biological molecule interaction

prediction [2], traﬃc forecasting [3], etc.

The current research on link prediction usually follows a kind of human

intuition that the more similar the attributes or topological structure of two

nodes are, the more likely that they have interactions with each other. Based

on the common similarity principle, several network similarity methods have

been proposed for link prediction task [4]. And they are designed by minimiz-

ing the pointwise mutual information (PMI) of co-occurring nodes in random

walk [5]. Besides, the idea of multi-level analysis is introduced to deal with

graph structure data from the local and global levels. TOME [6] proposes

two reﬁnement processes to obtain local information of cluster structure and

incorporates some global information into the matrix with path-based trans-

formation. Thereby, network similarity methods can also be classiﬁed from

multiple perspectives of the local and the global. The Node Clustering Co-

eﬃcient [7] evaluates the clustering coeﬃcients of all common neighbors of

the target node pair and sums them to obtain the ﬁnal similarity score of

the node pair. Such methods can eﬀectively handle link prediction task in

dynamic networks, such as traﬃc networks. Whereas, extracting only local

information will limit the ability to capture global similarities between nodes.

In contrast, other studies utilize global topological information of a network

to score the similarity of nodes, such as Katz [8], Random Walk with Restart

(RWR) [9], and Rooted Pagerank [10]. Except on sparsely unbalanced net-

works, the global structure based methods have shown better performance

than based on local information. Furthermore, the global methods are not

suitable for large-scale networks, specially with dense connections, due to

huge computational costs. In addition, the major challenge on these simi-

larity based methods does not avoid similarity measurement selection and

generalization limitation of a single index.

Obviously, another idea to improve the prediction accuracy can be de-

rived from edge information on graph to mine deeply the data to obtain

richer information. With the development of deep learning on graph data,

researchers pay more attention to graph representation learning methods with

the ability of learning graph topological information and enhancing node fea-

tures [11]. Specially, the feature learning process for the node is based on

the assumption that nodes with similar embedding representations will dis-

play similar structures. For example, HOGCN [2] adopts diﬀerent distance

features on neighbors and shows excellent robustness in sparse interaction

networks. Wang et al. [12] introduce the HAS method via Heterogeneous

graph data Augmentation and node Similarity to solve sparse imbalanced

link prediction. What’s more, it is noteworthy that the representation and

structure dual similarity assumption is not universal. For instance, some

proteins with similar characteristics but may have a lower probability of con-

nections [13]. To address such issues, SEAL [14] converts the link prediction

task into a graph classiﬁcation task by extracting the subgraphs around the

target links. Only the node information pooling is used to predict links in

SEAL, the loss of node information will bring disturbance to the accuracy

on prediction. Therefore, reducing the information loss has become another

challenge for current graph neural network-based methods.

In comparison, LGLP [15] transforms prediction task into a node classi-

ﬁcation task, by combining line graphs with graph neural networks for link

prediction to improve information transfer eﬃciency. LGLP can alleviate

the problem of ineﬃcient learning with sparse data, whereas the added edges

during information transfer may also bring in noise. So it will limit the

model’s performance to ignore the balance of diﬀerent levels of information.

Everything has two sides and the line graph transform is not an exception.

On dense graphs, the noise generated by the excessive edges of line graph

can adversely impact the prediction results [16]. By contrast, the informa-

tion generated by the increased edges of the transformation can improve the

prediction accuracy. So our motivation comes from how to make up for the

lack of line graph conversion and improve the performance by self-supervised

learning without additional information.

It is hard or expensive to acquire data labels in many practical appli-

cations, whereas contrastive learning is an excellent self-supervised learning

method to improve model performance with less labels. Current studies

focus on designing diverse graph augmentation strategies to yield various

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HighlightsLineGraphContrastiveLearningforLinkPredictionZehuaZhang,ShilinSun,GuixiangMa,CaimingZhongWedesignanovelcontrastivelearningframeworkbasedonlinegraphtobesuitableforlinkpredictiononsparseanddensegraphs.Weproposeacross-scalecontrastivelearningstrategytomaximizethemutualinformationbetweensubg...

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