  Graph neural networks (GNNs) are important tools for transductive learning
tasks, such as node classification in graphs, due to their expressive power in
capturing complex interdependency between nodes. To enable graph neural network
learning, existing works typically assume that labeled nodes, from two or
multiple classes, are provided, so that a discriminative classifier can be
learned from the labeled data. In reality, this assumption might be too
restrictive for applications, as users may only provide labels of interest in a
single class for a small number of nodes. In addition, most GNN models only
aggregate information from short distances (e.g., 1-hop neighbors) in each
round, and fail to capture long distance relationship in graphs. In this paper,
we propose a novel graph neural network framework, long-short distance
aggregation networks (LSDAN), to overcome these limitations. By generating
multiple graphs at different distance levels, based on the adjacency matrix, we
develop a long-short distance attention model to model these graphs. The direct
neighbors are captured via a short-distance attention mechanism, and neighbors
with long distance are captured by a long distance attention mechanism. Two
novel risk estimators are further employed to aggregate long-short-distance
networks, for PU learning and the loss is back-propagated for model learning.
Experimental results on real-world datasets demonstrate the effectiveness of
our algorithm.
