Graph Clustering with Graph Neural Networks

Abstract

Graph Neural Networks (GNNs) have achieved state-of-the-art results on many graph analysis tasks such as node classification and link prediction. However, important unsupervised problems on graphs, such as graph clustering, have proved more resistant to advances in GNNs. In this paper, we study unsupervised training of GNN pooling in terms of their clustering capabilities. We start by drawing a connection between graph clustering and graph pooling: intuitively, a good graph clustering is what one would expect from a GNN pooling layer. Counterintuitively, we show that this is not true for state-of-the-art pooling methods, such as MinCut pooling. To address these deficiencies, we introduce Deep Modularity Networks (DMON), an unsupervised pooling method inspired by the modularity measure of clustering quality, and show how it tackles recovery of the challenging clustering structure of real-world graphs. In order to clarify the regimes where existing methods fail, we carefully design a set of experiments on synthetic data which show that DMON is able to jointly leverage the signal from the graph structure and node attributes. Similarly, on real-world data, we show that DMON produces high quality clusters which correlate strongly with ground truth labels, achieving state-of-the-art results.

Learning to Model the Relationship Between Brain Structural and Functional Connectomes

“…From early spectral convolutions [15], [30] to distributed implementations of (equivalent) shift-invariant polynomial graph filters [19], [26], [31], GCNs integrate information from both the graph topology and nodal attributes to learn representations of network data. Indeed, the GRL paradigm is to learn low-dimensional embeddings of individual vertices, edges, or the graph itself [23], [32]- [34], which can then be used in e.g., (semi-supervised) node classification [15], link prediction [35], graph clustering [36], [37], and graph clas-sification [38]. Recently, GRL ideas have permeated to neuroimaging data analysis for behavioral state classification [39], to study the relationship between SC and FC [13], [40], and to extract representations for subject classification [41]- [43].…”

A Framework for Joint Unsupervised Learning of Cluster-Aware Embedding for Heterogeneous Networks

“…(1) The most basic approach is the unsupervised learning of the network embedding, followed by a clustering algorithm, e.g., K-Means or GMM, on the embedding. (2) Some architectures learn the network embedding with the primary objective to find good clustering assignments [47,48]. However, they usually do not perform well on downstream tasks such as node classification as the embeddings are primarily aimed to find clusters.…”

UCoDe: Unified Community Detection with Graph Convolutional Networks

“…Some GNNs directly optimize for non-overlapping community detection with community-wise loss functions. Single objective approaches propose variations of traditional cohesiveness scores, such as min-cut [3] and modularity [35]. Yet, single-objective methods inherit the limitations of the score they aim to optimize, providing community memberships that are subject to the loss objective's definition of community.…”

“…CommDGI's combined objective overcomes the limitations of the single score methods, but requires extensive parameter tuning for proper results. Although models like DMoN [35] return soft community assignments through a softmax output layer, both single and combined objective methods explicitly penalize overlaps among communities.…”

“…GNNs for non-overlapping community detection either optimize for a single score or combine several scores. Single score methods revisit traditional measures such as mincut [3] and modularity [35] objectives to return node-community probabilities. Combined score methods [46,47] integrate multiple different objectives.…”