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.

翻译：图神经网络旨在学习图结构数据的表示，并在节点分类等任务中展现出卓越性能。近年来，许多方法从优化目标和谱图理论的角度研究了图神经网络的表示。然而，主导表示学习的特征空间在图神经网络中尚未被系统研究。本文通过分析空间域和谱域模型的特征空间来填补这一空白。我们将其分解为确定性的特征空间和可训练权重，从而利用矩阵空间分析显式研究特征空间。特别地，我们理论发现重复聚合操作会导致特征空间趋于线性相关。基于这些发现，我们提出1）特征子空间平坦化与2）结构主成分来扩展特征空间。大量实验验证了所提出的更全面特征空间的有效性，其推理时间与基线相当，并展现出高效的收敛能力。