  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 protein in a protein-protein interaction
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. For example, in a social
network, a group of people with shared interests forms a user group, whereas a
number of user groups are interconnected via interactions or common members. We
study the node classification problem in the hierarchical graph where a `node'
is a graph instance, e.g., a user group in the above example. As labels are
usually limited in real-world data, we design two novel semi-supervised
solutions named \underline{SE}mi-supervised gr\underline{A}ph
c\underline{L}assification via \underline{C}autious/\underline{A}ctive
\underline{I}teration (or SEAL-C/AI in short). SEAL-C/AI adopt an iterative
framework that takes turns to build or update two classifiers, one working at
the graph instance level and the other at the hierarchical graph level. To
simplify the representation of the hierarchical graph, we propose a novel
supervised, self-attentive graph embedding method called SAGE, which embeds
graph instances of arbitrary size into fixed-length vectors. Through
experiments on synthetic data and Tencent QQ group data, we demonstrate that
SEAL-C/AI not only outperform competing methods by a significant margin in
terms of accuracy/Macro-F1, but also generate meaningful interpretations of the
learned representations.
