Exploring Graph Learning for Semi-Supervised Classification Beyond Euclidean Data

Semi-supervised classification on graph-structured data has received increasing attention, where labels are only available for a small subset of data such as social networks and citation networks. This problem is challenging due to the irregularity of graphs. Graph convolutional neural networks (GCN) have been recently proposed to address such kinds of problems, which feed the graph topology into the network to guide operations such as graph convolution. Nevertheless, in most cases where the graphs are not given, they are empirically constructed manually, which tends to be sub-optimal. Hence, we propose Graph Learning Neural Networks (GLNN), which exploits the optimization of graphs (the adjacency matrix in particular) and integrates into the GCN for semi-supervised node classification. Leveraging on spectral graph theory, this essentially combines both graph learning and graph convolution into a unified framework. Specifically, we represent features of social/citation networks as graph signals, and propose the objective of graph learning from the graph-signal prior, sparsity constraint and properties of a valid adjacency matrix via maximum a posteriori estimation. The optimization objective is then integrated into the loss function of the GCN, leading to joint learning of the adjacency matrix and high-level features. Experimental results show that our proposed GLNN outperforms state-of-the-art approaches over widely adopted social network datasets and citation network datasets.