Training graph neural networks (GNNs) on large-scale graphs can be challenging due to the high computational expense caused by the massive number of nodes and high-dimensional nodal features. Existing graph condensation studies tackle this problem only by reducing the number of nodes in the graph. However, the resulting condensed graph data can still be cumbersome. Specifically, although the nodes of the Citeseer dataset are reduced to 0.9% (30 nodes) in training, the number of features is 3,703, severely exceeding the training sample magnitude. Faced with this challenge, we study the problem of joint condensation for both features and nodes in large-scale graphs. This task is challenging mainly due to 1) the intertwined nature of the node features and the graph structure calls for the feature condensation solver to be structure-aware; and 2) the difficulty of keeping useful information in the condensed graph. To address these challenges, we propose a novel framework TinyGraph, to condense features and nodes simultaneously in graphs. Specifically, we cast the problem as matching the gradients of GNN weights trained on the condensed graph and the gradients obtained from training over the original graph, where the feature condensation is achieved by a trainable function. The condensed graph obtained by minimizing the matching loss along the training trajectory can henceforth retain critical information in the original graph. Extensive experiments were carried out to demonstrate the effectiveness of the proposed TinyGraph. For example, a GNN trained with TinyGraph retains 98.5% and 97.5% of the original test accuracy on the Cora and Citeseer datasets, respectively, while significantly reducing the number of nodes by 97.4% and 98.2%, and the number of features by 90.0% on both datasets.

用TinyGraph框架在大规模图上同时压缩特征和节点，通过匹配梯度实现特征压缩并保留关键信息，在减少节点和特征数量的同时仍能保持原始测试准确率的大部分。

TinyGraph: 图神经网络的特征和节点聚合