Node classification and graph classification are two graph learning problems that predict the class label of a node and the class label of a graph respectively. A node of a graph usually represents a real-world entity, e.g., a user in a social network, or a document in a document citation network. In this work, we consider a more challenging but practically useful setting, in which a node itself is a graph instance. This leads to a hierarchical graph perspective which arises in many domains such as social network, biological network and document collection. We study the node classification problem in the hierarchical graph where a 'node' is a graph instance. As labels are usually limited, we design a novel semi-supervised solution named SEAL-CI. SEAL-CI adopts an iterative framework that takes turns to update two modules, one working at the graph instance level and the other at the hierarchical graph level. To enforce a consistency among different levels of hierarchical graph, we propose the Hierarchical Graph Mutual Information (HGMI) and further present a way to compute HGMI with theoretical guarantee. We demonstrate the effectiveness of this hierarchical graph modeling and the proposed SEAL-CI method on text and social network data.

翻译：节点分类和图表分类是预测节点类标签和图表类标签的两个图表学习问题。图表的节点通常代表真实世界实体,例如社交网络中的用户,或文件引用网络中的文档。在这项工作中,我们考虑一个更具挑战性但实际有用的环境,节点本身是一个图形实例。这导致一个在社会网络、生物网络和文件收集等许多领域出现的等级图表视角。我们研究了“节点”是图表实例的等级图表中的节点分类问题。由于标签通常有限,我们设计了一个名为SEAL-CI的新型半监督性解决方案。SEAL-CI采用一个迭接框架,它转而用于更新两个模块,一个在图形实例一级工作,另一个在层次图形一级工作。为了在不同层次的层次图形之间实现一致性,我们建议了高层次图形相互信息(HGMI),并进一步提出一种方法,用以根据理论保证对HGMI进行计算。我们演示了这一等级图形模型的效能以及拟议的SEAL-方法在SEAL数据网络上的有效性。