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（GCN）是深度学习向图等非结构化数据扩展的重要进展，但GCN仍需预构建的图结构才能运行。为解决此问题，通常使用经典图（如k近邻图）初始化GCN。尽管构建k近邻图计算效率较高，但其构建的图可能不利于学习：在k近邻图中，节点被限制具有固定数量的边，且所有边权重相等。我们提出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变权重，从而增强学习效果。树的数目是rpForest中的超参数，我们通过谱分析将其设定在合理范围内。实验表明，与k近邻初始化相比，使用rpForest初始化GCN可获得更优结果。