Graph

Mathematics

Random graph

Mathematical proof

Geodesy

Machine learning

Mathematical analysis

Benchmark (surveying)

Artificial intelligence

Geography

Generalization

Stochastic gradient descent

Geometry

Computer science

Theoretical computer science

Scalability

Artificial neural network

Database

Convolutional neural network

IEEE Transactions on Pattern Analysis and Machine Intelligence

Graph Convolutional Networks (GCNs), as a prominent example of graph neural networks, are receiving extensive attention for their powerful capability in learning node representations on graphs. There are various extensions, either in sampling and/or node feature aggregation, to further improve GCNs' performance, scalability and applicability in various domains. Still, there is room for further improvements on learning efficiency because performing batch gradient descent using the full dataset for every training iteration, as unavoidable for training (vanilla) GCNs, is not a viable option for large graphs. The good potential of random features in speeding up the training phase in large-scale problems motivates us to consider carefully whether GCNs with random weights are feasible. To investigate theoretically and empirically this issue, we propose a novel model termed Graph Convolutional Networks with Random Weights (GCN-RW) by revising the convolutional layer with random filters and simultaneously adjusting the learning objective with regularized least squares loss. Theoretical analyses on the model's approximation upper bound, structure complexity, stability and generalization, are provided with rigorous mathematical proofs. The effectiveness and efficiency of GCN-RW are verified on semi-supervised node classification task with several benchmark datasets. Experimental results demonstrate that, in comparison with some state-of-the-art approaches, GCN-RW can achieve better or matched accuracies with less training time cost.

Are Graph Convolutional Networks With Random Weights Feasible?