text: 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.
  @cite_7: 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.
  @cite_21: Convolutional Neural Networks are extremely efficient architectures in image and audio recognition tasks, thanks to their ability to exploit the local translational invariance of signal classes over their domain. In this paper we consider possible generalizations of CNNs to signals defined on more general domains without the action of a translation group. In particular, we propose two constructions, one based upon a hierarchical clustering of the domain, and another based on the spectrum of the graph Laplacian. We show through experiments that for low-dimensional graphs it is possible to learn convolutional layers with a number of parameters independent of the input size, resulting in efficient deep architectures.
  @cite_24: We present graph attention networks (GATs), novel neural network architectures that operate on graph-structured data, leveraging masked self-attentional layers to address the shortcomings of prior methods based on graph convolutions or their approximations. By stacking layers in which nodes are able to attend over their neighborhoods' features, we enable (implicitly) specifying different weights to different nodes in a neighborhood, without requiring any kind of costly matrix operation (such as inversion) or depending on knowing the graph structure upfront. In this way, we address several key challenges of spectral-based graph neural networks simultaneously, and make our model readily applicable to inductive as well as transductive problems. Our GAT models have achieved or matched state-of-the-art results across four established transductive and inductive graph benchmarks: the Cora, Citeseer and Pubmed citation network datasets, as well as a protein-protein interaction dataset (wherein test graphs remain unseen during training).
  @cite_19: 
  @cite_23: 
  @cite_15: Graph-based semisupervised learning (GSSL) provides a promising paradigm for modeling the manifold structures that may exist in massive data sources in high-dimensional spaces. It has been shown effective in propagating a limited amount of initial labels to a large amount of unlabeled data, matching the needs of many emerging applications such as image annotation and information retrieval. In this paper, we provide reviews of several classical GSSL methods and a few promising methods in handling challenging issues often encountered in web-scale applications. First, to successfully incorporate the contaminated noisy labels associated with web data, label diagnosis and tuning techniques applied to GSSL are surveyed. Second, to support scalability to the gigantic scale (millions or billions of samples), recent solutions based on anchor graphs are reviewed. To help researchers pursue new ideas in this area, we also summarize a few popular data sets and software tools publicly available. Important open issues are discussed at the end to stimulate future research.
  @cite_20: 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.
  @cite_13: We present a scalable approach for semi-supervised learning on graph-structured data that is based on an efficient variant of convolutional neural networks which operate directly on graphs. We motivate the choice of our convolutional architecture via a localized first-order approximation of spectral graph convolutions. Our model scales linearly in the number of graph edges and learns hidden layer representations that encode both local graph structure and features of nodes. In a number of experiments on citation networks and on a knowledge graph dataset we demonstrate that our approach outperforms related methods by a significant margin.
  @cite_12: Deep Learning's recent successes have mostly relied on Convolutional Networks, which exploit fundamental statistical properties of images, sounds and video data: the local stationarity and multi-scale compositional structure, that allows expressing long range interactions in terms of shorter, localized interactions. However, there exist other important examples, such as text documents or bioinformatic data, that may lack some or all of these strong statistical regularities. In this paper we consider the general question of how to construct deep architectures with small learning complexity on general non-Euclidean domains, which are typically unknown and need to be estimated from the data. In particular, we develop an extension of Spectral Networks which incorporates a Graph Estimation procedure, that we test on large-scale classification problems, matching or improving over Dropout Networks with far less parameters to estimate.
summary: While graph structures are central tools for various learning tasks ( semi-supervised learning in @cite_15 @cite_13 ), how to design efficient graph convolution networks has become a popular research topic. Graph convolutional approaches are often categorized into spectral and non-spectral classes @cite_24 . The spectral approach first proposed by @cite_21 defines the convolution operation in Fourier domain. Later, @cite_12 enables localized filtering by applying efficient spectral filters, and @cite_19 employs Chebyshev expansion of the graph Laplacian to avoid the eigendecomposition. Recently, GCN is proposed in @cite_13 to simplify previous methods with first-order expansion and re-parameterization trick. Non-spectral approaches define convolution on graph by using the spatial connections directly. For instance, @cite_7 learns a weight matrix for each node degree, the work by @cite_20 defines multiple-hop neighborhoods by using the powers series of a transition matrix, and other authors @cite_23 extracted normalized neighborhoods that contain a fixed number of nodes.