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.

本文通过在统一的优化框架中理论讨论了传统浅层学习方法与基于图卷积网络（GCNs）的关系，并提出了三种简单但强大的图卷积方法，包括有监督方法OGC以及两种无监督方法GGC和其多尺度版本GGCM，最后通过大量实验证明了我们方法的有效性。

从聚类假设到图卷积：重新思考基于图的半监督学习