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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We introduce a convolutional neural network that operates directly on graphs. These networks allow end-to-end learning of prediction pipelines whose inputs are graphs of arbitrary size and shape. The architecture we present generalizes standard molecular feature extraction methods based on circular fingerprints. We show that these data-driven features are more interpretable, and have better predictive performance on a variety of tasks. We present diffusion-convolutional neural networks (DCNNs), a new model for graph-structured data. Through the introduction of a diffusion-convolution operation, we show how diffusion-based representations can be learned from graph-structured data and used as an effective basis for node classification. DCNNs have several attractive qualities, including a latent representation for graphical data that is invariant under isomorphism, as well as polynomial-time prediction and learning that can be represented as tensor operations and efficiently implemented on a GPU. Through several experiments with real structured datasets, we demonstrate that DCNNs are able to outperform probabilistic relational models and kernel-on-graph methods at relational node classification tasks. Numerous important problems can be framed as learning from graph data. We propose a framework for learning convolutional neural networks for arbitrary graphs. These graphs may be undirected, directed, and with both discrete and continuous node and edge attributes. Analogous to image-based convolutional networks that operate on locally connected regions of the input, we present a general approach to extracting locally connected regions from graphs. Using established benchmark data sets, we demonstrate that the learned feature representations are competitive with state of the art graph kernels and that their computation is highly efficient. The problem of extracting meaningful data through graph analysis spans a range of different fields, such as the internet, social networks, biological networks, and many others. The importance of being able to effectively mine and learn from such data continues to grow as more and more structured data become available. In this paper, we present a simple and scalable semi-supervised learning method for graph-structured data in which only a very small portion of the training data are labeled. To sufficiently embed the graph knowledge, our method performs graph convolution from different views of the raw data. In particular, a dual graph convolutional neural network method is devised to jointly consider the two essential assumptions of semi-supervised learning: (1) local consistency and (2) global consistency. Accordingly, two convolutional neural networks are devised to embed the local-consistency-based and global-consistency-based knowledge, respectively. Given the different data transformations from the two networks, we then introduce an unsupervised temporal loss function for the ensemble. In experiments using both unsupervised and supervised loss functions, our method outperforms state-of-the-art techniques on different datasets. Low-dimensional embeddings of nodes in large graphs have proved extremely useful in a variety of prediction tasks, from content recommendation to identifying protein functions. However, most existing approaches require that all nodes in the graph are present during training of the embeddings; these previous approaches are inherently transductive and do not naturally generalize to unseen nodes. Here we present GraphSAGE, a general, inductive framework that leverages node feature information (e.g., text attributes) to efficiently generate node embeddings. Instead of training individual embeddings for each node, we learn a function that generates embeddings by sampling and aggregating features from a node's local neighborhood. Our algorithm outperforms strong baselines on three inductive node-classification benchmarks: we classify the category of unseen nodes in evolving information graphs based on citation and Reddit post data, and we show that our algorithm generalizes to completely unseen graphs using a multi-graph dataset of protein-protein interactions. Supervised learning on molecules has incredible potential to be useful in chemistry, drug discovery, and materials science. Luckily, several promising and closely related neural network models invariant to molecular symmetries have already been described in the literature. These models learn a message passing algorithm and aggregation procedure to compute a function of their entire input graph. At this point, the next step is to find a particularly effective variant of this general approach and apply it to chemical prediction benchmarks until we either solve them or reach the limits of the approach. In this paper, we reformulate existing models into a single common framework we call Message Passing Neural Networks (MPNNs) and explore additional novel variations within this framework. Using MPNNs we demonstrate state of the art results on an important molecular property prediction benchmark; these results are strong enough that we believe future work should focus on datasets with larger molecules or more accurate ground truth labels.