Graph Convolutional Network (GCN) with the powerful capacity to explore graph-structural data has gained noticeable success in recent years. Nonetheless, most of the existing GCN-based models suffer from the notorious over-smoothing issue, owing to which shallow networks are extensively adopted. This may be problematic for complex graph datasets because a deeper GCN should be beneficial to propagating information across remote neighbors. Recent works have devoted effort to addressing over-smoothing problems, including establishing residual connection structure or fusing predictions from multi-layer models. Because of the indistinguishable embeddings from deep layers, it is reasonable to generate more reliable predictions before conducting the combination of outputs from various layers. In light of this, we propose an Alternating Graph-regularized Neural Network (AGNN) composed of Graph Convolutional Layer (GCL) and Graph Embedding Layer (GEL). GEL is derived from the graph-regularized optimization containing Laplacian embedding term, which can alleviate the over-smoothing problem by periodic projection from the low-order feature space onto the high-order space. With more distinguishable features of distinct layers, an improved Adaboost strategy is utilized to aggregate outputs from each layer, which explores integrated embeddings of multi-hop neighbors. The proposed model is evaluated via a large number of experiments including performance comparison with some multi-layer or multi-order graph neural networks, which reveals the superior performance improvement of AGNN compared with state-of-the-art models.

翻译：图卷积网络（GCN）凭借其探索图结构数据的强大能力，近年来取得了显著成功。然而，现有大多数基于GCN的模型都饱受臭名昭著的过平滑问题困扰，因此浅层网络被广泛采用。对于复杂图数据集而言，这可能存在问题，因为深层GCN本应有利于在远程邻域间传播信息。近期研究致力于解决过平滑问题，包括建立残差连接结构或融合多层模型的预测结果。由于深层嵌入特征难以区分，因此在融合各层输出前生成更可靠的预测是合理的。基于此，我们提出一种由图卷积层（GCL）和图嵌入层（GEL）组成的交替图正则化神经网络（AGNN）。GEL源自包含拉普拉斯嵌入项的图正则化优化，通过将低阶特征空间周期性投影到高阶空间，可缓解过平滑问题。利用不同层更具区分性的特征，采用改进的Adaboost策略聚合各层输出，从而探索多跳邻居的集成嵌入。通过大量实验（包括与若干多层或多阶图神经网络的性能对比）评估所提模型，结果表明相较于现有最优模型，AGNN具有更优的性能提升效果。