Graph convolutional networks (GCNs) were a great step towards extending deep learning to unstructured data such as graphs. But GCNs still need a constructed graph to work with. To solve this problem, classical graphs such as $k$-nearest neighbor are usually used to initialize the GCN. Although it is computationally efficient to construct $k$-nn graphs, the constructed graph might not be very useful for learning. In a $k$-nn graph, points are restricted to have a fixed number of edges, and all edges in the graph have equal weights. We present a new way to construct the graph and initialize the GCN. It is based on random projection forest (rpForest). rpForest enables us to assign varying weights on edges indicating varying importance, which enhanced the learning. The number of trees is a hyperparameter in rpForest. We performed spectral analysis to help us setting this parameter in the right range. In the experiments, initializing the GCN using rpForest provides better results compared to $k$-nn initialization.

翻译：图卷积网络（GCNs）是将深度学习推广到图等非结构化数据的重要进展，但GCN仍需构建好的图才能运作。为解决此问题，通常使用k近邻等经典图结构来初始化GCN。尽管构建k近邻图在计算上高效，但构建的图可能对学习帮助有限。在k近邻图中，每个点的边数固定，且所有边权重相等。我们提出了一种基于随机投影森林（rpForest）的图构建与GCN初始化新方法。rpForest能够为边分配反映不同重要性的可变权重，从而增强学习效果。rpForest中的树数量作为超参数，我们通过谱分析确定其合理取值范围。实验表明，相较于k近邻初始化，使用rpForest初始化GCN可取得更优结果。