Graph convolutional networks (GCNs) have been attracting widespread attentions due to their encouraging performance and powerful generalizations. However, few work provide a general view to interpret various GCNs and guide GCNs' designs. In this paper, by revisiting the original GCN, we induce an interpretable regularizer-centerd optimization framework, in which by building appropriate regularizers we can interpret most GCNs, such as APPNP, JKNet, DAGNN, and GNN-LF/HF. Further, under the proposed framework, we devise a dual-regularizer graph convolutional network (dubbed tsGCN) to capture topological and semantic structures from graph data. Since the derived learning rule for tsGCN contains an inverse of a large matrix and thus is time-consuming, we leverage the Woodbury matrix identity and low-rank approximation tricks to successfully decrease the high computational complexity of computing infinite-order graph convolutions. Extensive experiments on eight public datasets demonstrate that tsGCN achieves superior performance against quite a few state-of-the-art competitors w.r.t. classification tasks.

本文主要研究在图数据上检测拓扑和语义结构，提出了一种名为tsGCN的图卷积网络，通过可解释的正则化优化框架，成功减少了计算无限阶图卷积的高计算复杂度，并且在八个公共数据集上对分类任务取得了比同类竞争对手更卓越的性能。

超越图卷积网络：一种解释性的以正则化为中心的优化框架