  Recently, graph Convolutional Neural Networks (graph CNNs) have been widely
used for graph data representation and semi-supervised learning tasks. However,
existing graph CNNs generally use a fixed graph which may be not optimal for
semi-supervised learning tasks. In this paper, we propose a novel Graph
Learning-Convolutional Network (GLCN) for graph data representation and
semi-supervised learning. The aim of GLCN is to learn an optimal graph
structure that best serves graph CNNs for semi-supervised learning by
integrating both graph learning and graph convolution together in a unified
network architecture. The main advantage is that in GLCN, both given labels and
the estimated labels are incorporated and thus can provide useful 'weakly'
supervised information to refine (or learn) the graph construction and also to
facilitate the graph convolution operation in GLCN for unknown label
estimation. Experimental results on seven benchmarks demonstrate that GLCN
significantly outperforms state-of-the-art traditional fixed structure based
graph CNNs.
