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.
As analyzed above, most existing variants of GNN assume pairwise relationships between objects, while our work operates on a high-order hypergraph @cite_33 @cite_6 where the between-object relationships are beyond pairwise. Hypergraph learning methods differ in the structure of the hypergraph, , clique expansion and star expansion @cite_27 , and the definition of hypergraph Laplacians @cite_46 @cite_26 @cite_12 . Following @cite_35 , @cite_3 propose a hypergraph neural network using a Chebyshev expansion of the graph Laplacian . By analyzing the incident structure of a hypergraph, our work directly defines two differentiable operators, , hypergraph convolution and hypergraph attention, which is intuitive and flexible in learning more discriminative deep embeddings.
@cite_35 @cite_26 @cite_33 @cite_6 @cite_3 @cite_27 @cite_46 @cite_12
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In this paper, we present a hypergraph neural networks (HGNN) framework for data representation learning, which can encode high-order data correlation in a hypergraph structure. Confronting the challenges of learning representation for complex data in real practice, we propose to incorporate such data structure in a hypergraph, which is more flexible on data modeling, especially when dealing with complex data. In this method, a hyperedge convolution operation is designed to handle the data correlation during representation learning. In this way, traditional hypergraph learning procedure can be conducted using hyperedge convolution operations efficiently. HGNN is able to learn the hidden layer representation considering the high-order data structure, which is a general framework considering the complex data correlations. We have conducted experiments on citation network classification and visual object recognition tasks and compared HGNN with graph convolutional networks and other traditional methods. Experimental results demonstrate that the proposed HGNN method outperforms recent state-of-theart methods. We can also reveal from the results that the proposed HGNN is superior when dealing with multi-modal data compared with existing methods. A detailed understanding of expansion in complex networks can greatly aid in the design and analysis of algorithms for a variety of important network tasks, including routing messages, ranking nodes, and compressing graphs. This has motivated several recent investigations of expansion properties in real-world graphs and also in random models of real-world graphs, like the preferential attachment graph. The results point to a gap between real-world observations and theoretical models. Some real-world graphs are expanders and others are not, but a graph generated by the preferential attachment model is an expander whp. We study a random graph Gn that combines certain aspects of geometric random graphs and preferential attachment graphs. This model yields a graph with power-law degree distribution where the expansion property depends on a tunable parameter of the model. The vertices of Gn are n sequentially generated points x1, x2, ..., xn chosen uniformly at random from the unit sphere in R3. After generating xt, we randomly connect it to m points from those points in x1, x2, ..., xt-1.... Lots of learning tasks require dealing with graph data which contains rich relation information among elements. Modeling physics system, learning molecular fingerprints, predicting protein interface, and classifying diseases require a model to learn from graph inputs. In other domains such as learning from non-structural data like texts and images, reasoning on extracted structures, like the dependency tree of sentences and the scene graph of images, is an important research topic which also needs graph reasoning models. Graph neural networks (GNNs) are connectionist models that capture the dependence of graphs via message passing between the nodes of graphs. Unlike standard neural networks, graph neural networks retain a state that can represent information from its neighborhood with arbitrary depth. Although the primitive GNNs have been found difficult to train for a fixed point, recent advances in network architectures, optimization techniques, and parallel computation have enabled successful learning with them. In recent years, systems based on variants of graph neural networks such as graph convolutional network (GCN), graph attention network (GAT), gated graph neural network (GGNN) have demonstrated ground-breaking performance on many tasks mentioned above. In this survey, we provide a detailed review over existing graph neural network models, systematically categorize the applications, and propose four open problems for future research. In this paper, we develop a novel paradigm, namely hypergraph shift, to find robust graph modes by probabilistic voting strategy, which are semantically sound besides the self-cohesiveness requirement in forming graph modes. Unlike the existing techniques to seek graph modes by shifting vertices based on pair-wise edges (i.e, an edge with 2 ends), our paradigm is based on shifting high-order edges (hyperedges) to deliver graph modes. Specifically, we convert the problem of seeking graph modes as the problem of seeking maximizers of a novel objective function with the aim to generate good graph modes based on sifting edges in hypergraphs. As a result, the generated graph modes based on dense subhypergraphs may more accurately capture the object semantics besides the self-cohesiveness requirement. We also formally prove that our technique is always convergent. Extensive empirical studies on synthetic and real world data sets are conducted on clustering and graph matching. They demonstrate that our techniques significantly outperform the existing techniques.