The performances of GNNs for representation learning on the graph-structured data are generally limited to the issue that existing GNNs rely on one assumption, i. e., the original graph structure is reliable. However, since real-world graphs is inevitably noisy or incomplete, this assumption is often unrealistic. In this paper, we propose a structure learning graph convolutional networks (SLGCNs)to alleviate the issue from two aspects, and the proposed approach is applied to node classification. Specifically, the first is node features, we design a efficient-spectral-clustering  with anchors (ESC-ANCH) approach to efficiently aggregate feature representationsfrom all similar nodes , no matter how far away they are. The second is edges, our approach generates a re-connected adjacency matrix according to the similarities between nodes and optimized for the downstream prediction task so as to make up for the shortcomings of original adjacency matrix , considering that the original adjacency matrix usually provides misleading information for aggregation step of GCN in the graphs with low level of homophily. Both the re-connected adjacency matrix and original adjacency matrix are applied to SLGCNs to aggregate feature representations from nearby nodes . Thus, SLGCNs can be applied to graphs with various levels of homophily. Experimental results on a wide range of benchmark datasets illustrate that the proposed SLGCNs outperform the stat-of-the-art GNN counterparts.
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.
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