Graph neural networks aim to learn representations for graph-structured data
and show impressive performance, particularly in node classification. Recently,
many methods have studied the representations of GNNs from the perspective of
optimization goals and spectral graph theory. However, the feature space that
dominates representation learning has not been systematically studied in graph
neural networks. In this paper, we propose to fill this gap by analyzing the
feature space of both spatial and spectral models. We decompose graph neural
networks into determined feature spaces and trainable weights, providing the
convenience of studying the feature space explicitly using matrix space
analysis. In particular, we theoretically find that the feature space tends to
be linearly correlated due to repeated aggregations. Motivated by these
findings, we propose 1) feature subspaces flattening and 2) structural
principal components to expand the feature space. Extensive experiments verify
the effectiveness of our proposed more comprehensive feature space, with
comparable inference time to the baseline, and demonstrate its efficient
convergence capability.

本研究通过矩阵空间分析，系统地研究了空间模型与谱模型对于特征空间的影响，理论分析表明特征空间由于重复的聚合而趋向于线性相关，为此，我们提出了特征子空间展开和结构主成分等方法来扩展特征空间，实验表明我们的方法有效并能够提高收敛性能。