Existing Graph Convolutional Networks (GCNs) are shallow---the number of the layers is usually not larger than 2. The deeper variants by simply stacking more layers, unfortunately perform worse, even involving well-known tricks like weight penalizing, dropout, and residual connections. This paper reveals that developing deep GCNs mainly encounters two obstacles: and . The over-fitting issue weakens the generalization ability on small graphs, while over-smoothing impedes model training by isolating output representations from the input features with the increase in network depth. Hence, we propose DropEdge, a novel technique to alleviate both issues. At its core, DropEdge randomly removes a certain number of edges from the input graphs, acting like a data augmenter and also a message passing reducer. More importantly, DropEdge enables us to recast a wider range of Convolutional Neural Networks (CNNs) from the image field to the graph domain; in particular, we study DenseNet and InceptionNet in this paper. Extensive experiments on several benchmarks demonstrate that our method allows deep GCNs to achieve promising performance, even when the number of layers exceeds 30---the deepest GCN that has ever been proposed.
Inspired by the huge success of CNNs in computer vision, a large number of methods come redefining the notion of convolution on graphs under the umbrella of GCNs. The first prominent research on GCNs is presented in @cite_25 , which develops graph convolution based on spectral graph theory. Later, @cite_14 @cite_17 @cite_8 @cite_9 @cite_15 apply improvements, extensions, and approximations on spectral-based GCNs. With contending the scalability issue of spectral-based GCNs on large graphs, spatial-based GCNs have been rapidly developed @cite_5 @cite_24 @cite_31 @cite_11 . These methods directly perform convolution in the graph domain by aggregating the information from neighbor nodes. By recent, several sampling-based methods have been proposed for fast graph representation learning, including the node-wise sampling methods @cite_5 , the layer-wise approach @cite_7 and its layer-dependent variant @cite_28 .
@cite_31 @cite_14 @cite_11 @cite_7 @cite_8 @cite_28 @cite_9 @cite_24 @cite_5 @cite_15 @cite_25 @cite_17
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Graph Convolutional Networks (GCNs) have become a crucial tool on learning representations of graph vertices. The main challenge of adapting GCNs on large-scale graphs is the scalability issue that it incurs heavy cost both in computation and memory due to the uncontrollable neighborhood expansion across layers. In this paper, we accelerate the training of GCNs through developing an adaptive layer-wise sampling method. By constructing the network layer by layer in a top-down passway, we sample the lower layer conditioned on the top one, where the sampled neighborhoods are shared by different parent nodes and the over expansion is avoided owing to the fixed-size sampling. More importantly, the proposed sampler is adaptive and applicable for explicit variance reduction, which in turn enhances the training of our method. Furthermore, we propose a novel and economical approach to promote the message passing over distant nodes by applying skip connections. Intensive experiments on several benchmarks verify the effectiveness of our method regarding the classification accuracy while enjoying faster convergence speed. Convolutional neural networks (CNNs) have achieved great success on grid-like data such as images, but face tremendous challenges in learning from more generic data such as graphs. In CNNs, the trainable local filters enable the automatic extraction of high-level features. The computation with filters requires a fixed number of ordered units in the receptive fields. However, the number of neighboring units is neither fixed nor are they ordered in generic graphs, thereby hindering the applications of convolutional operations. Here, we address these challenges by proposing the learnable graph convolutional layer (LGCL). LGCL automatically selects a fixed number of neighboring nodes for each feature based on value ranking in order to transform graph data into grid-like structures in 1-D format, thereby enabling the use of regular convolutional operations on generic graphs. To enable model training on large-scale graphs, we propose a sub-graph training method to reduce the excessive memory and computational resource requirements suffered by prior methods on graph convolutions. Our experimental results on node classification tasks in both transductive and inductive learning settings demonstrate that our methods can achieve consistently better performance on the Cora, Citeseer, Pubmed citation network, and protein-protein interaction network datasets. Our results also indicate that the proposed methods using sub-graph training strategy are more efficient as compared to prior approaches. In this paper, we describe a novel deep convolutional neural network (CNN) that is deeper and wider than other existing deep networks for hyperspectral image classification. Unlike current state-of-the-art approaches in CNN-based hyperspectral image classification, the proposed network, called contextual deep CNN, can optimally explore local contextual interactions by jointly exploiting local spatio-spectral relationships of neighboring individual pixel vectors. The joint exploitation of the spatio-spectral information is achieved by a multi-scale convolutional filter bank used as an initial component of the proposed CNN pipeline. The initial spatial and spectral feature maps obtained from the multi-scale filter bank are then combined together to form a joint spatio-spectral feature map. The joint feature map representing rich spectral and spatial properties of the hyperspectral image is then fed through a fully convolutional network that eventually predicts the corresponding label of each pixel vector. The proposed approach is tested on three benchmark data sets: the Indian Pines data set, the Salinas data set, and the University of Pavia data set. Performance comparison shows enhanced classification performance of the proposed approach over the current state-of-the-art on the three data sets. Two architectures that generalize convolutional neural networks (CNNs) for the processing of signals supported on graphs are introduced. We start with the selection graph neural network (GNN), which replaces linear time invariant filters with linear shift invariant graph filters to generate convolutional features and reinterprets pooling as a possibly nonlinear subsampling stage where nearby nodes pool their information in a set of preselected sample nodes. A key component of the architecture is to remember the position of sampled nodes to permit computation of convolutional features at deeper layers. The second architecture, dubbed aggregation GNN, diffuses the signal through the graph and stores the sequence of diffused components observed by a designated node. This procedure effectively aggregates all components into a stream of information having temporal structure to which the convolution and pooling stages of regular CNNs can be applied. A multinode version of aggregation GNNs is further introduced for operation in large-scale graphs. An important property of selection and aggregation GNNs is that they reduce to conventional CNNs when particularized to time signals reinterpreted as graph signals in a circulant graph. Comparative numerical analyses are performed in a source localization application over synthetic and real-world networks. Performance is also evaluated for an authorship attribution problem and text category classification. Multinode aggregation GNNs are consistently the best-performing GNN architecture.