  Learning unbiased node representations for imbalanced samples in the graph
has become a more remarkable and important topic. For the graph, a significant
challenge is that the topological properties of the nodes (e.g., locations,
roles) are unbalanced (topology-imbalance), other than the number of training
labeled nodes (quantity-imbalance). Existing studies on topology-imbalance
focus on the location or the local neighborhood structure of nodes, ignoring
the global underlying hierarchical properties of the graph, i.e., hierarchy. In
the real-world scenario, the hierarchical structure of graph data reveals
important topological properties of graphs and is relevant to a wide range of
applications. We find that training labeled nodes with different hierarchical
properties have a significant impact on the node classification tasks and
confirm it in our experiments. It is well known that hyperbolic geometry has a
unique advantage in representing the hierarchical structure of graphs.
Therefore, we attempt to explore the hierarchy-imbalance issue for node
classification of graph neural networks with a novelty perspective of
hyperbolic geometry, including its characteristics and causes. Then, we propose
a novel hyperbolic geometric hierarchy-imbalance learning framework, named
HyperIMBA, to alleviate the hierarchy-imbalance issue caused by uneven
hierarchy-levels and cross-hierarchy connectivity patterns of labeled
nodes.Extensive experimental results demonstrate the superior effectiveness of
HyperIMBA for hierarchy-imbalance node classification tasks.
