  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.
