DEEP GRAPH-LEVEL CLUSTERING USING PSEUDO-LABEL-GUIDED MUTUAL INFORMATION MAXIMIZA-TION NETWORK

Abstract

In this work, we study the problem of partitioning a set of graphs into different groups such that the graphs in the same group are similar while the graphs in different groups are dissimilar. This problem was rarely studied previously, although there have been a lot of work on node clustering and graph classification. The problem is challenging because it is difficult to measure the similarity or distance between graphs. One feasible approach is using graph kernels to compute a similarity matrix for the graphs and then performing spectral clustering, but the effectiveness of existing graph kernels in measuring the similarity between graphs is very limited. To solve the problem, we propose a novel method called Deep Graph-Level Clustering (DGLC). DGLC utilizes a graph isomorphism network to learn graph-level representations by maximizing the mutual information between the representations of entire graphs and substructures, under the regularization of a clustering module that ensures discriminative representations via pseudo labels. DGLC achieves graph-level representation learning and graph-level clustering in an end-to-end manner. The experimental results on six benchmark datasets of graphs show that our DGLC has state-of-the-art performance in comparison to many baselines.

1. INTRODUCTION

Graph-structured data widely exist in real-world scenarios, such as social networks (Newman, 2006) and molecular analysis (Gilmer et al., 2017) . Compared to other data formats, graph data explicitly contain connections between data through the attributes of nodes and edges, which can provide rich structural information for many applications. In recent years, machine learning on graph-structured data gains more and more attention. Many supervised and unsupervised learning methods have been proposed for graph-structured data in various applications. The machine learning problems of graph-structured data can be organized into two categories: nodelevel learning and graph-level learning. In node-level learning, the samples are the nodes in a single graph. Node-level learning mainly includes node classification (Li et al., 2017; Wu et al., 2021; Xu et al., 2021) and node clustering (Wang et al., 2017; Pan & Kang, 2021; Lin et al., 2021) . Classical node classification methods are often based on graph embedding (Yan et al., 2006; Cai et al., 2018) and graph regularization (Subramanya & Bilmes, 2009; Bhagat et al., 2011) , while recent advances are based on graph neural networks (GNN) (Kipf & Welling, 2017; Xu et al., 2019; Wu et al., 2020) . Owing to the success of GNN in nodes classification, a few researchers have proposed GNN-based methods for nodes clustering (Wang et al., 2019; Bo et al., 2020; Zhu & Koniusz, 2021) . Different from node-level learning, in graph-level learning, the samples are a set of graphs that can be organized into different groups. Classical methods for graph-level classification are often based on graph kernels (Vishwanathan et al., 2010; Yanardag & Vishwanathan, 2015) while recent advances are based on GNN (Wu et al., 2020; Rong et al., 2020) . Researchers generally utilize various types of GNN, e.g., graph convolutional networks (GCNs) (Kipf & Welling, 2017) and graph isomorphism network (GIN) (Xu et al., 2019) to learn graph-level representations by aggregating inherent node information and structural neighbor information in graphs, then they train a classifier based on the learned graph-level representations (Zhang et al., 2018; Sun et al., 2020; Wang et al., 2021; Doshi 

