  Graph Neural Networks (GNNs) have shown superior performance for
semi-supervised learning of numerous web applications, such as classification
on web services and pages, analysis of online social networks, and
recommendation in e-commerce. The state of the art derives representations for
all nodes in graphs following the same diffusion (message passing) model
without discriminating their uniqueness. However, (i) labeled nodes involved in
model training usually account for a small portion of graphs in the
semisupervised setting, and (ii) different nodes locate at different graph
local contexts and it inevitably degrades the representation qualities if
treating them undistinguishedly in diffusion.
  To address the above issues, we develop NDM, a universal node-wise diffusion
model, to capture the unique characteristics of each node in diffusion, by
which NDM is able to yield high-quality node representations. In what follows,
we customize NDM for semisupervised learning and design the NIGCN model. In
particular, NIGCN advances the efficiency significantly since it (i) produces
representations for labeled nodes only and (ii) adopts well-designed neighbor
sampling techniques tailored for node representation generation. Extensive
experimental results on various types of web datasets, including citation,
social and co-purchasing graphs, not only verify the state-of-the-art
effectiveness of NIGCN but also strongly support the remarkable scalability of
NIGCN. In particular, NIGCN completes representation generation and training
within 10 seconds on the dataset with hundreds of millions of nodes and
billions of edges, up to orders of magnitude speedups over the baselines, while
achieving the highest F1-scores on classification.
