  Graph Convolutional Neural Networks (GCNNs) are generalizations of CNNs to
graph-structured data, in which convolution is guided by the graph topology. In
many cases where graphs are unavailable, existing methods manually construct
graphs or learn task-driven adaptive graphs. In this paper, we propose Graph
Learning Neural Networks (GLNNs), which exploit the optimization of graphs (the
adjacency matrix in particular) from both data and tasks. Leveraging on
spectral graph theory, we propose the objective of graph learning from a
sparsity constraint, properties of a valid adjacency matrix as well as a graph
Laplacian regularizer via maximum a posteriori estimation. The optimization
objective is then integrated into the loss function of the GCNN, which adapts
the graph topology to not only labels of a specific task but also the input
data. Experimental results show that our proposed GLNN outperforms
state-of-the-art approaches over widely adopted social network datasets and
citation network datasets for semi-supervised classification.
