  Graph-based semi-supervised learning (GSSL) has long been a hot research
topic. Traditional methods are generally shallow learners, based on the cluster
assumption. Recently, graph convolutional networks (GCNs) have become the
predominant techniques for their promising performance. In this paper, we
theoretically discuss the relationship between these two types of methods in a
unified optimization framework. One of the most intriguing findings is that,
unlike traditional ones, typical GCNs may not jointly consider the graph
structure and label information at each layer. Motivated by this, we further
propose three simple but powerful graph convolution methods. The first is a
supervised method OGC which guides the graph convolution process with labels.
The others are two unsupervised methods: GGC and its multi-scale version GGCM,
both aiming to preserve the graph structure information during the convolution
process. Finally, we conduct extensive experiments to show the effectiveness of
our methods.
