This paper introduces a generalization of Convolutional Neural Networks (CNNs) to graphs with irregular linkage structures, especially heterogeneous graphs with typed nodes and schemas. We propose a novel spatial convolution operation to model the key properties of local connectivity and translation invariance, using high-order connection patterns or motifs. We develop a novel deep architecture Motif-CNN that employs an attention model to combine the features extracted from multiple patterns, thus effectively capturing high-order structural and feature information. Our experiments on semi-supervised node classification on real-world social networks and multiple representative heterogeneous graph datasets indicate significant gains of 6-21% over existing graph CNNs and other state-of-the-art techniques.
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).
We present a new distributed representation in deep neural nets wherein the information is represented in native form as a matrix. This differs from current neural architectures that rely on vector representations. We consider matrices as central to the architecture and they compose the input, hidden and output layers. The model representation is more compact and elegant -- the number of parameters grows only with the largest dimension of the incoming layer rather than the number of hidden units. We derive several new deep networks: (i) feed-forward nets that map an input matrix into an output matrix, (ii) recurrent nets which map a sequence of input matrices into a sequence of output matrices. We also reinterpret existing models for (iii) memory-augmented networks and (iv) graphs using matrix notations. For graphs we demonstrate how the new notations lead to simple but effective extensions with multiple attentions. Extensive experiments on handwritten digits recognition, face reconstruction, sequence to sequence learning, EEG classification, and graph-based node classification demonstrate the efficacy and compactness of the matrix architectures.
We examine two fundamental tasks associated with graph representation learning: link prediction and semi-supervised node classification. We present a novel autoencoder architecture capable of learning a joint representation of both local graph structure and available node features for the multi-task learning of link prediction and node classification. Our autoencoder architecture is efficiently trained end-to-end in a single learning stage to simultaneously perform link prediction and node classification, whereas previous related methods require multiple training steps that are difficult to optimize. We provide a comprehensive empirical evaluation of our models on nine benchmark graph-structured datasets and demonstrate significant improvement over related methods for graph representation learning. Reference code and data are available at https://github.com/vuptran/graph-representation-learning
Graph Convolutional Networks (GCNs) have shown significant improvements in semi-supervised learning on graph-structured data. Concurrently, unsupervised learning of graph embeddings has benefited from the information contained in random walks. In this paper, we propose a model: Network of GCNs (N-GCN), which marries these two lines of work. At its core, N-GCN trains multiple instances of GCNs over node pairs discovered at different distances in random walks, and learns a combination of the instance outputs which optimizes the classification objective. Our experiments show that our proposed N-GCN model improves state-of-the-art baselines on all of the challenging node classification tasks we consider: Cora, Citeseer, Pubmed, and PPI. In addition, our proposed method has other desirable properties, including generalization to recently proposed semi-supervised learning methods such as GraphSAGE, allowing us to propose N-SAGE, and resilience to adversarial input perturbations.
Recently there has been a surge of interest in designing graph embedding methods. Few, if any, can scale to a large-sized graph with millions of nodes due to both computational complexity and memory requirements. In this paper, we relax this limitation by introducing the MultI-Level Embedding (MILE) framework -- a generic methodology allowing contemporary graph embedding methods to scale to large graphs. MILE repeatedly coarsens the graph into smaller ones using a hybrid matching technique to maintain the backbone structure of the graph. It then applies existing embedding methods on the coarsest graph and refines the embeddings to the original graph through a graph convolution neural network that it learns. The proposed MILE framework is agnostic to the underlying graph embedding techniques and can be applied to many existing graph embedding methods without modifying them. We employ our framework on several popular graph embedding techniques and conduct embedding for real-world graphs. Experimental results on five large-scale datasets demonstrate that MILE significantly boosts the speed (order of magnitude) of graph embedding while generating embeddings of better quality, for the task of node classification. MILE can comfortably scale to a graph with 9 million nodes and 40 million edges, on which existing methods run out of memory or take too long to compute on a modern workstation. Our code and data are publicly available with detailed instructions for adding new base embedding methods: \url{https://github.com/jiongqian/MILE}.
Methods that learn representations of nodes in a graph play a critical role in network analysis since they enable many downstream learning tasks. We propose Graph2Gauss - an approach that can efficiently learn versatile node embeddings on large scale (attributed) graphs that show strong performance on tasks such as link prediction and node classification. Unlike most approaches that represent nodes as point vectors in a low-dimensional continuous space, we embed each node as a Gaussian distribution, allowing us to capture uncertainty about the representation. Furthermore, we propose an unsupervised method that handles inductive learning scenarios and is applicable to different types of graphs: plain/attributed, directed/undirected. By leveraging both the network structure and the associated node attributes, we are able to generalize to unseen nodes without additional training. To learn the embeddings we adopt a personalized ranking formulation w.r.t. the node distances that exploits the natural ordering of the nodes imposed by the network structure. Experiments on real world networks demonstrate the high performance of our approach, outperforming state-of-the-art network embedding methods on several different tasks. Additionally, we demonstrate the benefits of modeling uncertainty - by analyzing it we can estimate neighborhood diversity and detect the intrinsic latent dimensionality of a graph.
Recent advances in the field of network embedding have shown the low-dimensional network representation is playing a critical role in network analysis. However, most of the existing principles of network embedding do not incorporate auxiliary information such as content and labels of nodes flexibly. In this paper, we take a matrix factorization perspective of network embedding, and incorporate structure, content and label information of the network simultaneously. For structure, we validate that the matrix we construct preserves high-order proximities of the network. Label information can be further integrated into the matrix via the process of random walk sampling to enhance the quality of embedding in an unsupervised manner, i.e., without leveraging downstream classifiers. In addition, we generalize the Skip-Gram Negative Sampling model to integrate the content of the network in a matrix factorization framework. As a consequence, network embedding can be learned in a unified framework integrating network structure and node content as well as label information simultaneously. We demonstrate the efficacy of the proposed model with the tasks of semi-supervised node classification and link prediction on a variety of real-world benchmark network datasets.
In this paper, we propose GPSP, a novel Graph Partition and Space Projection based approach, to learn the representation of a heterogeneous network that consists of multiple types of nodes and links. Concretely, we first partition the heterogeneous network into homogeneous and bipartite subnetworks. Then, the projective relations hidden in bipartite subnetworks are extracted by learning the projective embedding vectors. Finally, we concatenate the projective vectors from bipartite subnetworks with the ones learned from homogeneous subnetworks to form the final representation of the heterogeneous network. Extensive experiments are conducted on a real-life dataset. The results demonstrate that GPSP outperforms the state-of-the-art baselines in two key network mining tasks: node classification and clustering.
We present graph partition neural networks (GPNN), an extension of graph neural networks (GNNs) able to handle extremely large graphs. GPNNs alternate between locally propagating information between nodes in small subgraphs and globally propagating information between the subgraphs. To efficiently partition graphs, we experiment with several partitioning algorithms and also propose a novel variant for fast processing of large scale graphs. We extensively test our model on a variety of semi-supervised node classification tasks. Experimental results indicate that GPNNs are either superior or comparable to state-of-the-art methods on a wide variety of datasets for graph-based semi-supervised classification. We also show that GPNNs can achieve similar performance as standard GNNs with fewer propagation steps.
We propose a new network architecture, Gated Attention Networks (GaAN), for learning on graphs. Unlike the traditional multi-head attention mechanism, which equally consumes all attention heads, GaAN uses a convolutional sub-network to control each attention head's importance. We demonstrate the effectiveness of GaAN on the inductive node classification problem. Moreover, with GaAN as a building block, we construct the Graph Gated Recurrent Unit (GGRU) to address the traffic speed forecasting problem. Extensive experiments on three real-world datasets show that our GaAN framework achieves state-of-the-art results on both tasks.
Graphs are a fundamental abstraction for modeling relational data. However, graphs are discrete and combinatorial in nature, and learning representations suitable for machine learning tasks poses statistical and computational challenges. In this work, we propose Graphite, an algorithmic framework for unsupervised learning of representations over nodes in large graphs using deep latent variable generative models. Our model parameterizes variational autoencoders (VAE) with graph neural networks, and uses a novel iterative graph refinement strategy inspired by low-rank approximations for decoding. On a wide variety of synthetic and benchmark datasets, Graphite outperforms competing approaches for the tasks of density estimation, link prediction, and node classification. Finally, we derive a theoretical connection between message passing in graph neural networks and mean-field variational inference.
We generalize the scattering transform to graphs and consequently construct a convolutional neural network on graphs. We show that under certain conditions, any feature generated by such a network is approximately invariant to permutations and stable to graph manipulations. Numerical results demonstrate competitive performance on relevant 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 for previously unseen data. 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.
Network embedding methodologies, which learn a distributed vector representation for each vertex in a network, have attracted considerable interest in recent years. Existing works have demonstrated that vertex representation learned through an embedding method provides superior performance in many real-world applications, such as node classification, link prediction, and community detection. However, most of the existing methods for network embedding only utilize topological information of a vertex, ignoring a rich set of nodal attributes (such as, user profiles of an online social network, or textual contents of a citation network), which is abundant in all real-life networks. A joint network embedding that takes into account both attributional and relational information entails a complete network information and could further enrich the learned vector representations. In this work, we present Neural-Brane, a novel Neural Bayesian Personalized Ranking based Attributed Network Embedding. For a given network, Neural-Brane extracts latent feature representation of its vertices using a designed neural network model that unifies network topological information and nodal attributes; Besides, it utilizes Bayesian personalized ranking objective, which exploits the proximity ordering between a similar node-pair and a dissimilar node-pair. We evaluate the quality of vertex embedding produced by Neural-Brane by solving the node classification and clustering tasks on four real-world datasets. Experimental results demonstrate the superiority of our proposed method over the state-of-the-art existing methods.
Graph-structured data such as social networks, functional brain networks, gene regulatory networks, communications networks have brought the interest in generalizing deep learning techniques to graph domains. In this paper, we are interested to design neural networks for graphs with variable length in order to solve learning problems such as vertex classification, graph classification, graph regression, and graph generative tasks. Most existing works have focused on recurrent neural networks (RNNs) to learn meaningful representations of graphs, and more recently new convolutional neural networks (ConvNets) have been introduced. In this work, we want to compare rigorously these two fundamental families of architectures to solve graph learning tasks. We review existing graph RNN and ConvNet architectures, and propose natural extension of LSTM and ConvNet to graphs with arbitrary size. Then, we design a set of analytically controlled experiments on two basic graph problems, i.e. subgraph matching and graph clustering, to test the different architectures. Numerical results show that the proposed graph ConvNets are 3-17% more accurate and 1.5-4x faster than graph RNNs. Graph ConvNets are also 36% more accurate than variational (non-learning) techniques. Finally, the most effective graph ConvNet architecture uses gated edges and residuality. Residuality plays an essential role to learn multi-layer architectures as they provide a 10% gain of performance.
Graph representations have increasingly grown in popularity during the last years. Existing representation learning approaches explicitly encode network structure. Despite their good performance in downstream processes (e.g., node classification, link prediction), there is still room for improvement in different aspects, like efficacy, visualization, and interpretability. In this paper, we propose, t-PINE, a method that addresses these limitations. Contrary to baseline methods, which generally learn explicit graph representations by solely using an adjacency matrix, t-PINE avails a multi-view information graph, the adjacency matrix represents the first view, and a nearest neighbor adjacency, computed over the node features, is the second view, in order to learn explicit and implicit node representations, using the Canonical Polyadic (a.k.a. CP) decomposition. We argue that the implicit and the explicit mapping from a higher-dimensional to a lower-dimensional vector space is the key to learn more useful, highly predictable, and gracefully interpretable representations. Having good interpretable representations provides a good guidance to understand how each view contributes to the representation learning process. In addition, it helps us to exclude unrelated dimensions. Extensive experiments show that t-PINE drastically outperforms baseline methods by up to 158.6% with respect to Micro-F1, in several multi-label classification problems, while it has high visualization and interpretability utility.
The success of graph embeddings or node representation learning in a variety of downstream tasks, such as node classification, link prediction, and recommendation systems, has led to their popularity in recent years. Representation learning algorithms aim to preserve local and global network structure by identifying node neighborhood notions. However, many existing algorithms generate embeddings that fail to properly preserve the network structure, or lead to unstable representations due to random processes (e.g., random walks to generate context) and, thus, cannot generate to multi-graph problems. In this paper, we propose RECS, a novel, stable graph embedding algorithmic framework. RECS learns graph representations using connection subgraphs by employing the analogy of graphs with electrical circuits. It preserves both local and global connectivity patterns, and addresses the issue of high-degree nodes. Further, it exploits the strength of weak ties and meta-data that have been neglected by baselines. The experiments show that RECS outperforms state-of-the-art algorithms by up to 36.85% on multi-label classification problem. Further, in contrast to baselines, RECS, being deterministic, is completely stable.
Network embedding, which learns low-dimensional vector representation for nodes in the network, has attracted considerable research attention recently. However, the existing methods are incapable of handling billion-scale networks, because they are computationally expensive and, at the same time, difficult to be accelerated by distributed computing schemes. To address these problems, we propose RandNE (Iterative Random Projection Network Embedding), a novel and simple billion-scale network embedding method. Specifically, we propose a Gaussian random projection approach to map the network into a low-dimensional embedding space while preserving the high-order proximities between nodes. To reduce the time complexity, we design an iterative projection procedure to avoid the explicit calculation of the high-order proximities. Theoretical analysis shows that our method is extremely efficient, and friendly to distributed computing schemes without any communication cost in the calculation. We also design a dynamic updating procedure which can efficiently incorporate the dynamic changes of the networks without error aggregation. Extensive experimental results demonstrate the efficiency and efficacy of RandNE over state-of-the-art methods in several tasks including network reconstruction, link prediction and node classification on multiple datasets with different scales, ranging from thousands to billions of nodes and edges.
In network embedding, random walks play a fundamental role in preserving network structures. However, random walk based embedding methods have two limitations. First, random walk methods are fragile when the sampling frequency or the number of node sequences changes. Second, in disequilibrium networks such as highly biases networks, random walk methods often perform poorly due to the lack of global network information. In order to solve the limitations, we propose in this paper a network diffusion based embedding method. To solve the first limitation, our method employs a diffusion driven process to capture both depth information and breadth information. The time dimension is also attached to node sequences that can strengthen information preserving. To solve the second limitation, our method uses the network inference technique based on cascades to capture the global network information. To verify the performance, we conduct experiments on node classification tasks using the learned representations. Results show that compared with random walk based methods, diffusion based models are more robust when samplings under each node is rare. We also conduct experiments on a highly imbalanced network. Results shows that the proposed model are more robust under the biased network structure.