This paper theoretically discusses the relationship between conventional cluster-based shallow learning methods and the recently emerging graph convolutional neural networks (GCNs) in graph-based semi-supervised learning (GSSL) within a unified optimization framework. Specifically, we demonstrate that, unlike existing methods, conventional GCNs may not consider both graph structure and label information at each layer. Based on this, we propose three novel graph convolutional methods: OGC, a supervised learning method that utilizes label information; GGC, an unsupervised learning method that preserves graph structure; and its multi-scale version, GGCM. We demonstrate their effectiveness through extensive experiments. The source code is openly available.
