Graph Convolutional Networks (GCNs) have recently become the primary choice for learning from graph-structured data, superseding hash fingerprints in representing chemical compounds. However, GCNs lack the ability to take into account the ordering of node neighbors, even when there is a geometric interpretation of the graph vertices that provides an order based on their spatial positions. To remedy this issue, we propose Geometric Graph Convolutional Network (geo-GCN) which uses spatial features to efficiently learn from graphs that can be naturally located in space. Our contribution is threefold: we propose a GCN-inspired architecture which (i) leverages node positions, (ii) is a proper generalisation of both GCNs and Convolutional Neural Networks (CNNs), (iii) benefits from augmentation which further improves the performance and assures invariance with respect to the desired properties. Empirically, geo-GCN outperforms state-of-the-art graph-based methods on image classification and chemical tasks.

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图卷积网络(简称GCN),由Thomas Kpif于2017年在论文Semi-supervised classification with graph convolutional networks中提出。它为图(graph)结构数据的处理提供了一个崭新的思路,将深度学习中常用于图像的卷积神经网络应用到图数据上。

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Spectral clustering (SC) is a popular clustering technique to find strongly connected communities on a graph. SC can be used in Graph Neural Networks (GNNs) to implement pooling operations that aggregate nodes belonging to the same cluster. However, the eigendecomposition of the Laplacian is expensive and, since clustering results are graph-specific, pooling methods based on SC must perform a new optimization for each new sample. In this paper, we propose a graph clustering approach that addresses these limitations of SC. We formulate a continuous relaxation of the normalized minCUT problem and train a GNN to compute cluster assignments that minimize this objective. Our GNN-based implementation is differentiable, does not require to compute the spectral decomposition, and learns a clustering function that can be quickly evaluated on out-of-sample graphs. From the proposed clustering method, we design a graph pooling operator that overcomes some important limitations of state-of-the-art graph pooling techniques and achieves the best performance in several supervised and unsupervised tasks.

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Existing knowledge distillation methods focus on convolutional neural networks~(CNNs), where the input samples like images lie in a grid domain, and have largely overlooked graph convolutional networks~(GCN) that handle non-grid data. In this paper, we propose to our best knowledge the first dedicated approach to {distilling} knowledge from a pre-trained GCN model. To enable the knowledge transfer from the teacher GCN to the student, we propose a local structure preserving module that explicitly accounts for the topological semantics of the teacher. In this module, the local structure information from both the teacher and the student are extracted as distributions, and hence minimizing the distance between these distributions enables topology-aware knowledge transfer from the teacher, yielding a compact yet high-performance student model. Moreover, the proposed approach is readily extendable to dynamic graph models, where the input graphs for the teacher and the student may differ. We evaluate the proposed method on two different datasets using GCN models of different architectures, and demonstrate that our method achieves the state-of-the-art knowledge distillation performance for GCN models.

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Graph convolutional networks (GCNs) have recently become one of the most powerful tools for graph analytics tasks in numerous applications, ranging from social networks and natural language processing to bioinformatics and chemoinformatics, thanks to their ability to capture the complex relationships between concepts. At present, the vast majority of GCNs use a neighborhood aggregation framework to learn a continuous and compact vector, then performing a pooling operation to generalize graph embedding for the classification task. These approaches have two disadvantages in the graph classification task: (1)when only the largest sub-graph structure ($k$-hop neighbor) is used for neighborhood aggregation, a large amount of early-stage information is lost during the graph convolution step; (2) simple average/sum pooling or max pooling utilized, which loses the characteristics of each node and the topology between nodes. In this paper, we propose a novel framework called, dual attention graph convolutional networks (DAGCN) to address these problems. DAGCN automatically learns the importance of neighbors at different hops using a novel attention graph convolution layer, and then employs a second attention component, a self-attention pooling layer, to generalize the graph representation from the various aspects of a matrix graph embedding. The dual attention network is trained in an end-to-end manner for the graph classification task. We compare our model with state-of-the-art graph kernels and other deep learning methods. The experimental results show that our framework not only outperforms other baselines but also achieves a better rate of convergence.

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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 that a model learns 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 graph convolutional network (GCN) and 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.

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Graph convolutional networks (GCNs) have been successfully applied in node classification tasks of network mining. However, most of these models based on neighborhood aggregation are usually shallow and lack the "graph pooling" mechanism, which prevents the model from obtaining adequate global information. In order to increase the receptive field, we propose a novel deep Hierarchical Graph Convolutional Network (H-GCN) for semi-supervised node classification. H-GCN first repeatedly aggregates structurally similar nodes to hyper-nodes and then refines the coarsened graph to the original to restore the representation for each node. Instead of merely aggregating one- or two-hop neighborhood information, the proposed coarsening procedure enlarges the receptive field for each node, hence more global information can be learned. Comprehensive experiments conducted on public datasets demonstrate the effectiveness of the proposed method over the state-of-art methods. Notably, our model gains substantial improvements when only a few labeled samples are provided.

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Graph Convolutional Networks (GCNs) have proved to be a most powerful architecture in aggregating local neighborhood information for individual graph nodes. Low-rank proximities and node features are successfully leveraged in existing GCNs, however, attributes that graph links may carry are commonly ignored, as almost all of these models simplify graph links into binary or scalar values describing node connectedness. In our paper instead, links are reverted to hypostatic relationships between entities with descriptional attributes. We propose GCN-LASE (GCN with Link Attributes and Sampling Estimation), a novel GCN model taking both node and link attributes as inputs. To adequately captures the interactions between link and node attributes, their tensor product is used as neighbor features, based on which we define several graph kernels and further develop according architectures for LASE. Besides, to accelerate the training process, the sum of features in entire neighborhoods are estimated through Monte Carlo method, with novel sampling strategies designed for LASE to minimize the estimation variance. Our experiments show that LASE outperforms strong baselines over various graph datasets, and further experiments corroborate the informativeness of link attributes and our model's ability of adequately leveraging them.

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Many real-world problems can be represented as graph-based learning problems. In this paper, we propose a novel framework for learning spatial and attentional convolution neural networks on arbitrary graphs. Different from previous convolutional neural networks on graphs, we first design a motif-matching guided subgraph normalization method to capture neighborhood information. Then we implement subgraph-level self-attentional layers to learn different importances from different subgraphs to solve graph classification problems. Analogous to image-based attentional convolution networks that operate on locally connected and weighted regions of the input, we also extend graph normalization from one-dimensional node sequence to two-dimensional node grid by leveraging motif-matching, and design self-attentional layers without requiring any kinds of cost depending on prior knowledge of the graph structure. Our results on both bioinformatics and social network datasets show that we can significantly improve graph classification benchmarks over traditional graph kernel and existing deep models.

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Graph Convolutional Networks (GCNs) and their variants have experienced significant attention and have become the de facto methods for learning graph representations. GCNs derive inspiration primarily from recent deep learning approaches, and as a result, may inherit unnecessary complexity and redundant computation. In this paper, we reduce this excess complexity through successively removing nonlinearities and collapsing weight matrices between consecutive layers. We theoretically analyze the resulting linear model and show that it corresponds to a fixed low-pass filter followed by a linear classifier. Notably, our experimental evaluation demonstrates that these simplifications do not negatively impact accuracy in many downstream applications. Moreover, the resulting model scales to larger datasets, is naturally interpretable, and yields up to two orders of magnitude speedup over FastGCN.

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Graph Neural Networks (GNNs) for representation learning of graphs broadly follow a neighborhood aggregation framework, where the representation vector of a node is computed by recursively aggregating and transforming feature vectors of its neighboring nodes. Many GNN variants have been proposed and have achieved state-of-the-art results on both node and graph classification tasks. However, despite GNNs revolutionizing graph representation learning, there is limited understanding of their representational properties and limitations. Here, we present a theoretical framework for analyzing the expressive power of GNNs in capturing different graph structures. Our results characterize the discriminative power of popular GNN variants, such as Graph Convolutional Networks and GraphSAGE, and show that they cannot learn to distinguish certain simple graph structures. We then develop a simple architecture that is provably the most expressive among the class of GNNs and is as powerful as the Weisfeiler-Lehman graph isomorphism test. We empirically validate our theoretical findings on a number of graph classification benchmarks, and demonstrate that our model achieves state-of-the-art performance.

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Graph Convolutional Neural Networks (Graph CNNs) are generalizations of classical CNNs to handle graph data such as molecular data, point could and social networks. Current filters in graph CNNs are built for fixed and shared graph structure. However, for most real data, the graph structures varies in both size and connectivity. The paper proposes a generalized and flexible graph CNN taking data of arbitrary graph structure as input. In that way a task-driven adaptive graph is learned for each graph data while training. To efficiently learn the graph, a distance metric learning is proposed. Extensive experiments on nine graph-structured datasets have demonstrated the superior performance improvement on both convergence speed and predictive accuracy.

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