Recently proposed Graph Neural Networks (GNNs) for vertex clustering are trained with an unsupervised minimum cut objective, approximated by a Spectral Clustering (SC) relaxation. However, the SC relaxation is loose and, while it offers a closed-form solution, it also yields overly smooth cluster assignments that poorly separate the vertices. In this paper, we propose a GNN model that computes cluster assignments by optimizing a tighter relaxation of the minimum cut based on graph total variation (GTV). The cluster assignments can be used directly to perform vertex clustering or to implement graph pooling in a graph classification framework. Our model consists of two core components: i) a message-passing layer that minimizes the $\ell_1$ distance in the features of adjacent vertices, which is key to achieving sharp transitions between clusters; ii) an unsupervised loss function that minimizes the GTV of the cluster assignments while ensuring balanced partitions. Experimental results show that our model outperforms other GNNs for vertex clustering and graph classification.

翻译：近期提出的用于顶点聚类的图神经网络（GNN）采用无监督最小割目标进行训练，并通过谱聚类（SC）松弛进行近似。然而，SC松弛条件较弱，尽管能提供闭式解，但会导致聚类分配过于平滑，难以有效分离顶点。本文提出一种基于图总变差（GTV）优化最小割更紧松弛的GNN模型，可直接利用聚类分配进行顶点聚类或在图分类框架中实现图池化。模型包含两个核心组件：i) 消息传递层，通过最小化相邻顶点特征的$\ell_1$距离实现聚类间锐利过渡；ii) 无监督损失函数，通过最小化聚类分配的GTV确保平衡划分。实验结果表明，本模型在顶点聚类和图分类任务中均优于其他GNN方法。