Graph clustering is a fundamental and challenging task in the field of graph
mining where the objective is to group the nodes into clusters taking into
consideration the topology of the graph. It has several applications in diverse
domains spanning social network analysis, recommender systems, computer vision,
and bioinformatics. In this work, we propose a novel method, DGCluster, which
primarily optimizes the modularity objective using graph neural networks and
scales linearly with the graph size. Our method does not require the number of
clusters to be specified as a part of the input and can also leverage the
availability of auxiliary node level information. We extensively test DGCluster
on several real-world datasets of varying sizes, across multiple popular
cluster quality metrics. Our approach consistently outperforms the
state-of-the-art methods, demonstrating significant performance gains in almost
all settings.

通过使用图神经网络优化模块性目标的 DGCluster 方法，我们在多个领域中进行图聚类，取得了显著的性能提升。

DGCLUSTER：一种基于模块化最大化的属性图聚类的神经框架

DGCLUSTER: A Neural Framework for Attributed Graph Clustering via  Modularity Maximization

Notions of community quality underlie network clustering. While studies
surrounding network clustering are increasingly common, a precise understanding
of the realtionship between different cluster quality metrics is unknown. In
this paper, we examine the relationship between stand-alone cluster quality
metrics and information recovery metrics through a rigorous analysis of four
widely-used network clustering algorithms -- Louvain, Infomap, label
propagation, and smart local moving. We consider the stand-alone quality
metrics of modularity, conductance, and coverage, and we consider the
information recovery metrics of adjusted Rand score, normalized mutual
information, and a variant of normalized mutual information used in previous
work. Our study includes both synthetic graphs and empirical data sets of sizes
varying from 1,000 to 1,000,000 nodes.
We find significant differences among the results of the different cluster
quality metrics. For example, clustering algorithms can return a value of 0.4
out of 1 on modularity but score 0 out of 1 on information recovery. We find
conductance, though imperfect, to be the stand-alone quality metric that best
indicates performance on information recovery metrics. Our study shows that the
variant of normalized mutual information used in previous work cannot be
assumed to differ only slightly from traditional normalized mutual information.
Smart local moving is the best performing algorithm in our study, but
discrepancies between cluster evaluation metrics prevent us from declaring it
absolutely superior. Louvain performed better than Infomap in nearly all the
tests in our study, contradicting the results of previous work in which Infomap
was superior to Louvain. We find that although label propagation performs
poorly when clusters are less clearly defined, it scales efficiently and
accurately to large graphs with well-defined clusters.

本文通过对四个广泛使用的网络聚类算法的严格分析，研究了独立集群质量指标和信息恢复度量之间的关系，并发现不同集群质量度量的结果存在显着差异，其中 conductance 是最能表明信息恢复度量性能的单独质量度量，但这也存在缺陷。在人工合成图和不同规模的实际数据集上的实验表明，Smart Local Moving 算法的表现最佳，但是各个算法的聚类评估指标的差异需要进行更多的研究。