Many real-world systems can be represented as graphs where the different entities are presented by nodes and their interactions by edges. An important task in studying large datasets is graph clustering. While there has been a lot of work on graph clustering using the connectivity between the nodes, many real-world networks also have node attributes. Clustering attributed graphs requires joint modeling of graph structure and node attributes. Recent work has focused on graph convolutional networks and graph convolutional filters to combine structural and content information. However, these methods are mostly limited to lowpass filtering and do not explicitly optimize the filters for the clustering task. In this paper, we introduce a graph signal processing based approach, where we design polynomial graph filters optimized for clustering. The proposed approach is formulated as a two-step iterative optimization problem where graph filters that are interpretable and optimal for the given data are learned while maximizing the separation between different clusters. The proposed approach is evaluated on attributed networks and compared to the state-of-the-art graph convolutional network approaches.
翻译:许多真实世界的系统可以作为图表来表示,其中不同的实体通过节点和边缘的相互作用来显示。研究大型数据集的一个重要任务是图形群集。虽然使用节点之间的连接对图形群集做了大量工作,但许多真实世界的网络也有节点属性。归结的图表需要共同建模图形结构和节点属性。最近的工作侧重于图变网络和图变过滤器,以将结构和内容信息结合起来。然而,这些方法大多局限于低通过滤器,并不明确优化集束任务的过滤器。在本文件中,我们采用了基于图形的信号处理法,我们在此设计以优化组合为主的多面图过滤器。拟议的方法是一个双步迭式优化问题,在其中学习了可解释的图形过滤器和对给定数据最优的优化,同时最大限度地将不同组群分解。拟议的方法是按被归并比较了点化的网络和状态的图变相网络方法。