Spectral clustering (SC) is a popular clustering technique to find strongly connected communities on a graph. SC can be used in Graph Neural Networks (GNNs) to implement pooling operations that aggregate nodes belonging to the same cluster. However, the eigendecomposition of the Laplacian is expensive and, since clustering results are graph-specific, pooling methods based on SC must perform a new optimization for each new sample. In this paper, we propose a graph clustering approach that addresses these limitations of SC. We formulate a continuous relaxation of the normalized minCUT problem and train a GNN to compute cluster assignments that minimize this objective. Our GNN-based implementation is differentiable, does not require to compute the spectral decomposition, and learns a clustering function that can be quickly evaluated on out-of-sample graphs. From the proposed clustering method, we design a graph pooling operator that overcomes some important limitations of state-of-the-art graph pooling techniques and achieves the best performance in several supervised and unsupervised tasks.

翻译：光谱群集(SC)是一种在图表上找到紧密关联社区的流行集成技术。 星体群集可以用于图形神经网络(GNNS),以实施属于同一组群的聚合节点的集合操作。 然而,拉普拉西亚星体的银共化成本昂贵,而且,由于集成结果针对图表,基于SC的集合方法必须对每个新样本进行新的优化。在本文中,我们提出了一个解决SC的这些局限性的图形集成方法。我们设计了一个普通化的最小化点集成问题,并训练一个GNNN来计算最小化这一目标的集成任务。我们基于GNN的落实是不同的,不需要对光谱分解进行计算,并且学习一个可快速评估外光谱图的集群功能。我们从拟议的组合方法中设计了一个图形集成操作器,以克服状态的图形集成技术的某些重大限制,并在若干受监管和未监督的任务中实现最佳性。