GCN-SL: Graph Convolutional Networks with Structure Learning for Graphs under Heterophily

In representation learning on the graph-structured data, under heterophily (or low homophily), many popular GNNs may fail to capture long-range dependencies, which leads to their performance degradation. To solve the above-mentioned issue, we propose a graph convolutional networks with structure learning (GCN-SL), and furthermore, the proposed approach can be applied to node classification. The proposed GCN-SL contains two improvements: corresponding to node features and edges, respectively. In the aspect of node features, we propose an efficient-spectral-clustering (ESC) and an ESC with anchors (ESC-ANCH) algorithms to efficiently aggregate feature representations from all similar nodes. In the aspect of edges, we build a re-connected adjacency matrix by using a special data preprocessing technique and similarity learning, and the re-connected adjacency matrix can be optimized directly along with GCN-SL parameters. Considering that the original adjacency matrix may provide misleading information for aggregation in GCN, especially the graphs being with a low level of homophily. The proposed GCN-SL can aggregate feature representations from nearby nodes via re-connected adjacency matrix and is applied to graphs with various levels of homophily. Experimental results on a wide range of benchmark datasets illustrate that the proposed GCN-SL outperforms the stateof-the-art GNN counterparts.