  An undirected weighted graph (UWG) is frequently adopted to describe the
interactions among a solo set of nodes from real applications, such as the user
contact frequency from a social network services system. A graph convolutional
network (GCN) is widely adopted to perform representation learning to a UWG for
subsequent pattern analysis tasks such as clustering or missing data
estimation. However, existing GCNs mostly neglects the latent collaborative
information hidden in its connected node pairs. To address this issue, this
study proposes to model the node collaborations via a symmetric latent factor
analysis model, and then regards it as a node-collaboration module for
supplementing the collaboration loss in a GCN. Based on this idea, a
Node-collaboration-informed Graph Convolutional Network (NGCN) is proposed with
three-fold ideas: a) Learning latent collaborative information from the
interaction of node pairs via a node-collaboration module; b) Building the
residual connection and weighted representation propagation to obtain high
representation capacity; and c) Implementing the model optimization in an
end-to-end fashion to achieve precise representation to the target UWG.
Empirical studies on UWGs emerging from real applications demonstrate that
owing to its efficient incorporation of node-collaborations, the proposed NGCN
significantly outperforms state-of-the-art GCNs in addressing the task of
missing weight estimation. Meanwhile, its good scalability ensures its
compatibility with more advanced GCN extensions, which will be further
investigated in our future studies.
