  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.
