GCN-SL: Graph Convolutional Network with Structure Learning for Disassortative Graphs

In representation learning on the graph-structured data, many popular GNNs may fail to capture long-range dependencies, which leads to their performance degradation. Furthermore, this weakness will be magnified when the concerned graph is disassortative. To solve the above-mentioned issue, we propose a graph convolutional network 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 edges and node features, respectively. Since the original adjacency matrix may provide misleading information for the aggregation process in GNNs, especially in the disassortative graph. We build a re-connected adjacency matrix by structure learning from the perspective of edges. The structure learning module aims to learn an optimized graph structure and corresponding feature representations. Specifically, the re-connected adjacency matrix is built by using a special data preprocessing technique and similarity learning, and can be optimized directly along with GCN-SL parameters. Through structure learning, GCN-SL can search reliable adjacent nodes from the entire graph for aggregation. In the aspect of node features, we propose an efficient-spectral-clustering (ESC) and an ESC with anchors (ESC-ANCH) algorithms. The two algorithms can efficiently aggregate feature representations from similar nodes, no matter how far away these similar nodes are from the target node. Both of the two improvements can help GCN-SL capture long-range dependencies, then make GCN-SL is capable of performing representation learning on both disassortative and assortative graphs. Experimental results on a wide range of benchmark datasets illustrate that the proposed GCN-SL outperforms the state-of-the-art GNN counterparts.