Recently, graph neural networks have attracted great attention and achieved prominent performance in various research fields. Most of those algorithms have assumed pairwise relationships of objects of interest. However, in many real applications, the relationships between objects are in higher-order, beyond a pairwise formulation. To efficiently learn deep embeddings on the high-order graph-structured data, we introduce two end-to-end trainable operators to the family of graph neural networks, i.e., hypergraph convolution and hypergraph attention. Whilst hypergraph convolution defines the basic formulation of performing convolution on a hypergraph, hypergraph attention further enhances the capacity of representation learning by leveraging an attention module. With the two operators, a graph neural network is readily extended to a more flexible model and applied to diverse applications where non-pairwise relationships are observed. Extensive experimental results with semi-supervised node classification demonstrate the effectiveness of hypergraph convolution and hypergraph attention.
Meanwhile, some spatial algorithms directly perform convolution on the graph. For instance, @cite_14 learn different parameters for nodes with different degrees, then average the intermediate embeddings over the neighborhood structures. @cite_63 propose the PATCHY-SAN architecture, which selects a fixed-length sequence of nodes as the receptive field and generate local normalized neighborhood representations for each of the nodes in the sequence. @cite_39 demonstrate that diffusion-based representations can serve as an effective basis for node classification. @cite_2 further explore a joint usage of diffusion and adjacency basis in a dual graph convolutional network. @cite_10 defines a unified framework via a message passing function, where each vertex sends messages based on its states and updates the states based on the message of its immediate neighbors. @cite_15 propose GraphSAGE, which customizes three aggregating functions, , element-wise mean, long short-term memory and pooling, to learn embeddings in an inductive setting.
@cite_14 @cite_39 @cite_63 @cite_2 @cite_15 @cite_10
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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. We notice information flow in convolutional neural networks is restricted inside local neighborhood regions due to the physical design of convolutional filters, which limits the overall understanding of complex scenes. In this paper, we propose the point-wise spatial attention network (PSANet) to relax the local neighborhood constraint. Each position on the feature map is connected to all the other ones through a self-adaptively learned attention mask. Moreover, information propagation in bi-direction for scene parsing is enabled. Information at other positions can be collected to help the prediction of the current position and vice versa, information at the current position can be distributed to assist the prediction of other ones. Our proposed approach achieves top performance on various competitive scene parsing datasets, including ADE20K, PASCAL VOC 2012 and Cityscapes, demonstrating its effectiveness and generality. Following the success of deep convolutional networks in various vision and speech related tasks, researchers have started investigating generalizations of the well-known technique for graph-structured data. A recently-proposed method called Graph Convolutional Networks has been able to achieve state-of-the-art results in the task of node classification. However, since the proposed method relies on localized first-order approximations of spectral graph convolutions, it is unable to capture higher-order interactions between nodes in the graph. In this work, we propose a motif-based graph attention model, called Motif Convolutional Networks (MCNs), which generalizes past approaches by using weighted multi-hop motif adjacency matrices to capture higher-order neighborhoods. A novel attention mechanism is used to allow each individual node to select the most relevant neighborhood to apply its filter. Experiments show that our proposed method is able to achieve state-of-the-art results on the semi-supervised node classification task. We propose an unsupervised method for learning multi-stage hierarchies of sparse convolutional features. While sparse coding has become an increasingly popular method for learning visual features, it is most often trained at the patch level. Applying the resulting filters convolutionally results in highly redundant codes because overlapping patches are encoded in isolation. By training convolutionally over large image windows, our method reduces the redudancy between feature vectors at neighboring locations and improves the efficiency of the overall representation. In addition to a linear decoder that reconstructs the image from sparse features, our method trains an efficient feed-forward encoder that predicts quasi-sparse features from the input. While patch-based training rarely produces anything but oriented edge detectors, we show that convolutional training produces highly diverse filters, including center-surround filters, corner detectors, cross detectors, and oriented grating detectors. We show that using these filters in multistage convolutional network architecture improves performance on a number of visual recognition and detection tasks.