Simple graph convolution (SGC) achieves competitive classification accuracy to graph convolutional networks (GCNs) in various tasks while being computationally more efficient and fitting fewer parameters. However, the width of SGC is narrow due to the over-smoothing of SGC with higher power, which limits the learning ability of graph representations. Here, we propose AdjMix, a simple and attentional graph convolutional model, that is scalable to wider structure and captures more nodes features information, by simultaneously mixing the adjacency matrices of different powers. We point out that the key factor of over-smoothing is the mismatched weights of adjacency matrices, and design AdjMix to address the over-smoothing of SGC and GCNs by adjusting the weights to matching values. Experiments on citation networks including Pubmed, Citeseer, and Cora show that our AdjMix improves over SGC by 2.4%, 2.2%, and 3.2%, respectively, while achieving same performance in terms of parameters and complexity, and obtains better performance in terms of classification accuracy, parameters, and complexity, compared to other baselines.
Real-time and realistic rendering of forest is an important and a difficult work in computer graphics and digital forestry. An image based real-time and realistic forestrendering software is developed in this paper. Three orthogonal billboards are used to represent the geometry and material of a tree, so that the 3D perception is enhanced and weak parallax of usual images based approaches is avoided. Shadows of all trees on the plat ground are generated through the stencil buffer, shadow projection and a mixture of the shadow with grass texture. Different billboards are chosen on the viewing direction and the lighting direction, so that the effect of object torsion due to poor image direction is avoided. Forest growth, forest rendering in different lighting conditions, navigation inside a forest, and flying over a forest are all simulated.
Existing popular methods for semi-supervised node classification with high-order convolution improve the learning ability of graph convolutional networks (GCNs) by capturing the feature information from high-order neighborhoods. However, these methods with high-order convolution usually require many parameters and high computational complexity. To address these limitations, we propose HCNP, a new higher-order GCN for semi-supervised node learning tasks, which can simultaneously aggregate information of various neighborhoods by constructing high-order convolution. In HCNP, we reduce the number of parameters using a weight sharing mechanism and combine the neighborhood information via multi-scale neighborhood pooling. Further, HCNP does not require a large number of hidden units, and it fits a few parameters and exhibits low complexity. We show that HCNP matches GCNs in terms of complexity and parameters. Comprehensive evaluations on publication citation datasets (Citeseer, Pubmed, and Cora) demonstrate that the proposed methods outperform MixHop in most cases while maintaining lower complexity and fewer parameters and achieve state-of-the-art performance in terms of accuracy and parameters compared to other baselines.INDEX TERMS High-order convolution, graph convolutional networks, weight sharing, multi-scale neighborhood pooling, higher-order graph convolutional network, semi-supervised node classification.
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