  Node Importance Estimation (NIE) is a task of inferring importance scores of
the nodes in a graph. Due to the availability of richer data and knowledge,
recent research interests of NIE have been dedicating to knowledge graphs for
predicting future or missing node importance scores. Existing state-of-the-art
NIE methods train the model by available labels, and they consider every
interested node equally before training. However, the nodes with higher
importance often require or receive more attention in real-world scenarios,
e.g., people may care more about the movies or webpages with higher importance.
To this end, we introduce Label Informed ContrAstive Pretraining (LICAP) to the
NIE problem for being better aware of the nodes with high importance scores.
Specifically, LICAP is a novel type of contrastive learning framework that aims
to fully utilize the continuous labels to generate contrastive samples for
pretraining embeddings. Considering the NIE problem, LICAP adopts a novel
sampling strategy called top nodes preferred hierarchical sampling to first
group all interested nodes into a top bin and a non-top bin based on node
importance scores, and then divide the nodes within top bin into several finer
bins also based on the scores. The contrastive samples are generated from those
bins, and are then used to pretrain node embeddings of knowledge graphs via a
newly proposed Predicate-aware Graph Attention Networks (PreGAT), so as to
better separate the top nodes from non-top nodes, and distinguish the top nodes
within top bin by keeping the relative order among finer bins. Extensive
experiments demonstrate that the LICAP pretrained embeddings can further boost
the performance of existing NIE methods and achieve the new state-of-the-art
performance regarding both regression and ranking metrics. The source code for
reproducibility is available at https://github.com/zhangtia16/LICAP
