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.

Although convolutional neural networks (CNNs) have shown good performance on grid data, they are limited in the semantic segmentation of irregular point clouds. This article proposes a novel and effective graph CNN framework, referred to as the local-global graph convolutional method (LGGCM), which can achieve short- and long-range dependencies on point clouds. The key to this framework is the design of local spatial attention convolution (LSA-Conv). The design includes two parts: generating a weighted adjacency matrix of the local graph composed of neighborhood points, and updating and aggregating the features of nodes to obtain the spatial geometric features of the local point cloud. In addition, a smooth module for central points is incorporated into the process of LSA-Conv to enhance the robustness of the convolution against noise interference by adjusting the position coordinates of the points adaptively. The learned robust LSA-Conv features are then fed into a global spatial attention module with the gated unit to extract long-range contextual information and dynamically adjust the weights of features from different stages. The proposed framework, consisting of both encoding and decoding branches, is an end-to-end trainable network for semantic segmentation of 3-D point clouds. The theoretical analysis of the approximation capabilities of LSA-Conv is discussed to determine whether the features of the point cloud can be accurately represented. Experimental results on challenging benchmarks of the 3-D point cloud demonstrate that the proposed framework achieves excellent performance.