Recently there has been increased interest in semi-supervised classification in the presence of graphical information. A new class of learning models has emerged that relies, at its most basic level, on classifying the data after first applying a graph convolution. To understand the merits of this approach, we study the classification of a mixture of Gaussians, where the data corresponds to the node attributes of a stochastic block model. We show that graph convolution extends the regime in which the data is linearly separable by a factor of roughly $1/\sqrt{D}$, where $D$ is the expected degree of a node, as compared to the mixture model data on its own. Furthermore, we find that the linear classifier obtained by minimizing the cross-entropy loss after the graph convolution generalizes to out-of-distribution data where the unseen data can have different intra- and inter-class edge probabilities from the training data.

该研究探讨了在图形信息存在的情况下，基于图卷积进行数据分类的方法，发现图卷积扩展了数据线性可分的范围，并且在最小化交叉熵损失后，得到的线性分类器具有很好的泛化能力。

半监督分类的图卷积：改进的线性可分性和越界泛化