  Knowledge representation of graph-based systems is fundamental across many
disciplines. To date, most existing methods for representation learning
primarily focus on networks with simplex labels, yet real-world objects (nodes)
are inherently complex in nature and often contain rich semantics or labels,
e.g., a user may belong to diverse interest groups of a social network,
resulting in multi-label networks for many applications. The multi-label
network nodes not only have multiple labels for each node, such labels are
often highly correlated making existing methods ineffective or fail to handle
such correlation for node representation learning. In this paper, we propose a
novel multi-label graph convolutional network (ML-GCN) for learning node
representation for multi-label networks. To fully explore label-label
correlation and network topology structures, we propose to model a multi-label
network as two Siamese GCNs: a node-node-label graph and a label-label-node
graph. The two GCNs each handle one aspect of representation learning for nodes
and labels, respectively, and they are seamlessly integrated under one
objective function. The learned label representations can effectively preserve
the inner-label interaction and node label properties, and are then aggregated
to enhance the node representation learning under a unified training framework.
Experiments and comparisons on multi-label node classification validate the
effectiveness of our proposed approach.
