In this work, we study semi-supervised multi-label node classification problem in attributed graphs. Classic solutions to multi-label node classification follow two steps, first learn node embedding and then build a node classifier on the learned embedding. To improve the discriminating power of the node embedding, we propose a novel collaborative graph walk, named Multi-Label-Graph-Walk, to finely tune node representations with the available label assignments in attributed graphs via reinforcement learning. The proposed method formulates the multi-label node classification task as simultaneous graph walks conducted by multiple label-specific agents. Furthermore, policies of the label-wise graph walks are learned in a cooperative way to capture first the predictive relation between node labels and structural attributes of graphs; and second, the correlation among the multiple label-specific classification tasks. A comprehensive experimental study demonstrates that the proposed method can achieve significantly better multi-label classification performance than the state-of-the-art approaches and conduct more efficient graph exploration.
Convolutional Neural Networks (CNNs) have been very successful at solving a variety of computer vision tasks such as object classification and detection, semantic segmentation, activity understanding, to name just a few. One key enabling factor for their great performance has been the ability to train very deep networks. Despite their huge success in many tasks, CNNs do not work well with non-Euclidean data, which is prevalent in many real-world applications. Graph Convolutional Networks (GCNs) offer an alternative that allows for non-Eucledian data input to a neural network. While GCNs already achieve encouraging results, they are currently limited to architectures with a relatively small number of layers, primarily due to vanishing gradients during training. This work transfers concepts such as residual/dense connections and dilated convolutions from CNNs to GCNs in order to successfully train very deep GCNs. We show the benefit of using deep GCNs (with as many as 112 layers) experimentally across various datasets and tasks. Specifically, we achieve very promising performance in part segmentation and semantic segmentation on point clouds and in node classification of protein functions across biological protein-protein interaction (PPI) graphs. We believe that the insights in this work will open avenues for future research on GCNs and their application to further tasks not explored in this paper. The source code for this work is available at https://github.com/lightaime/deep_gcns_torch and https://github.com/lightaime/deep_gcns for PyTorch and TensorFlow implementation respectively.
Towards the challenging problem of semi-supervised node classification, there have been extensive studies. As a frontier, Graph Neural Networks (GNNs) have aroused great interest recently, which update the representation of each node by aggregating information of its neighbors. However, most GNNs have shallow layers with a limited receptive field and may not achieve satisfactory performance especially when the number of labeled nodes is quite small. To address this challenge, we innovatively propose a graph few-shot learning (GFL) algorithm that incorporates prior knowledge learned from auxiliary graphs to improve classification accuracy on the target graph. Specifically, a transferable metric space characterized by a node embedding and a graph-specific prototype embedding function is shared between auxiliary graphs and the target, facilitating the transfer of structural knowledge. Extensive experiments and ablation studies on four real-world graph datasets demonstrate the effectiveness of our proposed model.
From social networks to protein complexes to disease genomes to visual data, hypergraphs are everywhere. However, the scope of research studying deep learning on hypergraphs is still quite sparse and nascent, as there has not yet existed an effective, unified framework for using hyperedge and vertex embeddings jointly in the hypergraph context, despite a large body of prior work that has shown the utility of deep learning over graphs and sets. Building upon these recent advances, we propose \textit{Deep Hyperedges} (DHE), a modular framework that jointly uses contextual and permutation-invariant vertex membership properties of hyperedges in hypergraphs to perform classification and regression in transductive and inductive learning settings. In our experiments, we use a novel random walk procedure and show that our model achieves and, in most cases, surpasses state-of-the-art performance on benchmark datasets. Additionally, we study our framework's performance on a variety of diverse, non-standard hypergraph datasets and propose several avenues of future work to further enhance DHE.
Graph kernels are kernel methods measuring graph similarity and serve as a standard tool for graph classification. However, the use of kernel methods for node classification, which is a related problem to graph representation learning, is still ill-posed and the state-of-the-art methods are heavily based on heuristics. Here, we present a novel theoretical kernel-based framework for node classification that can bridge the gap between these two representation learning problems on graphs. Our approach is motivated by graph kernel methodology but extended to learn the node representations capturing the structural information in a graph. We theoretically show that our formulation is as powerful as any positive semidefinite kernels. To efficiently learn the kernel, we propose a novel mechanism for node feature aggregation and a data-driven similarity metric employed during the training phase. More importantly, our framework is flexible and complementary to other graph-based deep learning models, e.g., Graph Convolutional Networks (GCNs). We empirically evaluate our approach on a number of standard node classification benchmarks, and demonstrate that our model sets the new state of the art.
We present GraphMix, a regularization method for Graph Neural Network based semi-supervised object classification, whereby we propose to train a fully-connected network jointly with the graph neural network via parameter sharing and interpolation-based regularization. Further, we provide a theoretical analysis of how GraphMix improves the generalization bounds of the underlying graph neural network, without making any assumptions about the "aggregation" layer or the depth of the graph neural networks. We experimentally validate this analysis by applying GraphMix to various architectures such as Graph Convolutional Networks, Graph Attention Networks and Graph-U-Net. Despite its simplicity, we demonstrate that GraphMix can consistently improve or closely match state-of-the-art performance using even simpler architectures such as Graph Convolutional Networks, across three established graph benchmarks: Cora, Citeseer and Pubmed citation network datasets, as well as three newly proposed datasets: Cora-Full, Co-author-CS and Co-author-Physics.
Graph convolutional neural networks (GCN) have been the model of choice for graph representation learning, which is mainly due to the effective design of graph convolution that computes the representation of a node by aggregating those of its neighbors. However, existing GCN variants commonly use 1-D graph convolution that solely operates on the object link graph without exploring informative relational information among object attributes. This significantly limits their modeling capability and may lead to inferior performance on noisy and sparse real-world networks. In this paper, we explore 2-D graph convolution to jointly model object links and attribute relations for graph representation learning. Specifically, we propose a computationally efficient dimensionwise separable 2-D graph convolution (DSGC) for filtering node features. Theoretically, we show that DSGC can reduce intra-class variance of node features on both the object dimension and the attribute dimension to learn more effective representations. Empirically, we demonstrate that by modeling attribute relations, DSGC achieves significant performance gain over state-of-the-art methods for node classification and clustering on a variety of real-world networks. The source code for reproducing the experimental results is available at https://github.com/liqimai/DSGC.
Representation learning on graphs has been gaining attention due to its wide applicability in predicting missing links, and classifying and recommending nodes. Most embedding methods aim to preserve certain properties of the original graph in the low dimensional space. However, real world graphs have a combination of several properties which are difficult to characterize and capture by a single approach. In this work, we introduce the problem of graph representation ensemble learning and provide a first of its kind framework to aggregate multiple graph embedding methods efficiently. We provide analysis of our framework and analyze -- theoretically and empirically -- the dependence between state-of-the-art embedding methods. We test our models on the node classification task on four real world graphs and show that proposed ensemble approaches can outperform the state-of-the-art methods by up to 8% on macro-F1. We further show that the approach is even more beneficial for underrepresented classes providing an improvement of up to 12%.
This paper studies the problem of cross-network node classification to overcome the insufficiency of labeled data in a single network. It aims to leverage the label information in a partially labeled source network to assist node classification in a completely unlabeled or partially labeled target network. Existing methods for single network learning cannot solve this problem due to the domain shift across networks. Some multi-network learning methods heavily rely on the existence of cross-network connections, thus are inapplicable for this problem. To tackle this problem, we propose a novel \textcolor{black}{graph} transfer learning framework AdaGCN by leveraging the techniques of adversarial domain adaptation and graph convolution. It consists of two components: a semi-supervised learning component and an adversarial domain adaptation component. The former aims to learn class discriminative node representations with given label information of the source and target networks, while the latter contributes to mitigating the distribution divergence between the source and target domains to facilitate knowledge transfer. Extensive empirical evaluations on real-world datasets show that AdaGCN can successfully transfer class information with a low label rate on the source network and a substantial divergence between the source and target domains. The source code for reproducing the experimental results is available at https://github.com/daiquanyu/AdaGCN.
Advancing research in the emerging field of deep graph learning requires new tools to support tensor computation over graphs. In this paper, we present the design principles and implementation of Deep Graph Library (DGL). DGL distills the computational patterns of GNNs into a few generalized sparse tensor operations suitable for extensive parallelization. By advocating graph as the central programming abstraction, DGL can perform optimizations transparently. By cautiously adopting a framework-neutral design, DGL allows users to easily port and leverage the existing components across multiple deep learning frameworks. Our evaluation shows that DGL significantly outperforms other popular GNN-oriented frameworks in both speed and memory consumption over a variety of benchmarks and has little overhead for small scale workloads.
Machine learning techniques for road networks hold the potential to facilitate many important transportation applications. Graph Convolutional Networks (GCNs) are neural networks that are capable of leveraging the structure of a road network by utilizing information of, e.g., adjacent road segments. While state-of-the-art GCNs target node classification tasks in social, citation, and biological networks, machine learning tasks in road networks differ substantially from such tasks. In road networks, prediction tasks concern edges representing road segments, and many tasks involve regression. In addition, road networks differ substantially from the networks assumed in the GCN literature in terms of the attribute information available and the network characteristics. Many implicit assumptions of GCNs do therefore not apply. We introduce the notion of Relational Fusion Network (RFN), a novel type of GCN designed specifically for machine learning on road networks. In particular, we propose methods that outperform state-of-the-art GCNs on both a road segment regression task and a road segment classification task by 32-40% and 21-24%, respectively. In addition, we provide experimental evidence of the short-comings of state-of-the-art GCNs in the context of road networks: unlike our method, they cannot effectively leverage the road network structure for road segment classification and fail to outperform a regular multi-layer perceptron.
Network Embedding is the task of learning continuous node representations for networks, which has been shown effective in a variety of tasks such as link prediction and node classification. Most of existing works aim to preserve different network structures and properties in low-dimensional embedding vectors, while neglecting the existence of noisy information in many real-world networks and the overfitting issue in the embedding learning process. Most recently, generative adversarial networks (GANs) based regularization methods are exploited to regularize embedding learning process, which can encourage a global smoothness of embedding vectors. These methods have very complicated architecture and suffer from the well-recognized non-convergence problem of GANs. In this paper, we aim to introduce a more succinct and effective local regularization method, namely adversarial training, to network embedding so as to achieve model robustness and better generalization performance. Firstly, the adversarial training method is applied by defining adversarial perturbations in the embedding space with an adaptive $L_2$ norm constraint that depends on the connectivity pattern of node pairs. Though effective as a regularizer, it suffers from the interpretability issue which may hinder its application in certain real-world scenarios. To improve this strategy, we further propose an interpretable adversarial training method by enforcing the reconstruction of the adversarial examples in the discrete graph domain. These two regularization methods can be applied to many existing embedding models, and we take DeepWalk as the base model for illustration in the paper. Empirical evaluations in both link prediction and node classification demonstrate the effectiveness of the proposed methods.
Low-dimensional embeddings of knowledge graphs and behavior graphs have proved remarkably powerful in varieties of tasks, from predicting unobserved edges between entities to content recommendation. The two types of graphs can contain distinct and complementary information for the same entities/nodes. However, previous works focus either on knowledge graph embedding or behavior graph embedding while few works consider both in a unified way. Here we present BEM , a Bayesian framework that incorporates the information from knowledge graphs and behavior graphs. To be more specific, BEM takes as prior the pre-trained embeddings from the knowledge graph, and integrates them with the pre-trained embeddings from the behavior graphs via a Bayesian generative model. BEM is able to mutually refine the embeddings from both sides while preserving their own topological structures. To show the superiority of our method, we conduct a range of experiments on three benchmark datasets: node classification, link prediction, triplet classification on two small datasets related to Freebase, and item recommendation on a large-scale e-commerce dataset.
Many researchers both in academia and industry have long been interested in the stock market. Numerous approaches were developed to accurately predict future trends in stock prices. Recently, there has been a growing interest in utilizing graph-structured data in computer science research communities. Methods that use relational data for stock market prediction have been recently proposed, but they are still in their infancy. First, the quality of collected information from different types of relations can vary considerably. No existing work has focused on the effect of using different types of relations on stock market prediction or finding an effective way to selectively aggregate information on different relation types. Furthermore, existing works have focused on only individual stock prediction which is similar to the node classification task. To address this, we propose a hierarchical attention network for stock prediction (HATS) which uses relational data for stock market prediction. Our HATS method selectively aggregates information on different relation types and adds the information to the representations of each company. Specifically, node representations are initialized with features extracted from a feature extraction module. HATS is used as a relational modeling module with initialized node representations. Then, node representations with the added information are fed into a task-specific layer. Our method is used for predicting not only individual stock prices but also market index movements, which is similar to the graph classification task. The experimental results show that performance can change depending on the relational data used. HATS which can automatically select information outperformed all the existing methods.
Graph neural networks (GNNs) are widely used in many applications. However, their robustness against adversarial attacks is criticized. Prior studies show that using unnoticeable modifications on graph topology or nodal features can significantly reduce the performances of GNNs. It is very challenging to design robust graph neural networks against poisoning attack and several efforts have been taken. Existing work aims at reducing the negative impact from adversarial edges only with the poisoned graph, which is sub-optimal since they fail to discriminate adversarial edges from normal ones. On the other hand, clean graphs from similar domains as the target poisoned graph are usually available in the real world. By perturbing these clean graphs, we create supervised knowledge to train the ability to detect adversarial edges so that the robustness of GNNs is elevated. However, such potential for clean graphs is neglected by existing work. To this end, we investigate a novel problem of improving the robustness of GNNs against poisoning attacks by exploring clean graphs. Specifically, we propose PA-GNN, which relies on a penalized aggregation mechanism that directly restrict the negative impact of adversarial edges by assigning them lower attention coefficients. To optimize PA-GNN for a poisoned graph, we design a meta-optimization algorithm that trains PA-GNN to penalize perturbations using clean graphs and their adversarial counterparts, and transfers such ability to improve the robustness of PA-GNN on the poisoned graph. Experimental results on four real-world datasets demonstrate the robustness of PA-GNN against poisoning attacks on graphs. Code and data are available here: https://github.com/tangxianfeng/PA-GNN.
We study the problem of end-to-end learning from complex multigraphs with potentially very large numbers of edges between two vertices, each edge labeled with rich information. Examples range from communication networks to flights between airports or financial transaction graphs. We propose Latent-Graph Convolutional Networks (L-GCNs), which propagate information from these complex edges to a latent adjacency tensor, after which further downstream tasks can be performed, such as node classification. We evaluate the performance of several variations of the model on two synthetic datasets simulating fraud in financial transaction networks, ensuring the model must make use of edge labels in order to achieve good classification performance. We find that allowing for nonlinear interactions on a per-neighbor basis boosts performance significantly, while showing promising results in an inductive setting. Finally, we demonstrate the use of L-GCNs on real-world data in the form of an urban transportation network.
The design of deep graph models still remains to be investigated and the crucial part is how to explore and exploit the knowledge from different hops of neighbors in an efficient way. In this paper, we propose a novel RNN-like deep graph neural network architecture by incorporating AdaBoost into the computation of network; and the proposed graph convolutional network called AdaGCN~(Adaboosting Graph Convolutional Network) has the ability to efficiently extract knowledge from high-order neighbors of current nodes and then integrates knowledge from different hops of neighbors into the network in an Adaboost way. Different from other graph neural networks that directly stack many graph convolution layers, AdaGCN shares the same base neural network architecture among all ``layers'' and is recursively optimized, which is similar to an RNN. Besides, We also theoretically established the connection between AdaGCN and existing graph convolutional methods, presenting the benefits of our proposal. Finally, extensive experiments demonstrate the consistent state-of-the-art prediction performance on graphs across different label rates and the computational advantage of our approach AdaGCN~\footnote{Code is available at \url{https://github.com/datake/AdaGCN}.}
Signed networks contain both positive and negative kinds of interactions like friendship and enmity. The task of node classification in non-signed graphs has proven to be beneficial in many real world applications, yet extensions to signed networks remain largely unexplored. In this paper we introduce the first analysis of node classification in signed social networks via diffuse interface methods based on the Ginzburg-Landau functional together with different extensions of the graph Laplacian to signed networks. We show that blending the information from both positive and negative interactions leads to performance improvement in real signed social networks, consistently outperforming the current state of the art.
\emph{Over-fitting} and \emph{over-smoothing} are two main obstacles of developing deep Graph Convolutional Networks (GCNs) for node classification. In particular, over-fitting weakens the generalization ability on small dataset, while over-smoothing impedes model training by isolating output representations from the input features with the increase in network depth. This paper proposes DropEdge, a novel and flexible technique to alleviate both issues. At its core, DropEdge randomly removes a certain number of edges from the input graph at each training epoch, acting like a data augmenter and also a message passing reducer. Furthermore, we theoretically demonstrate that DropEdge either reduces the convergence speed of over-smoothing or relieves the information loss caused by it. More importantly, our DropEdge is a general skill that can be equipped with many other backbone models (e.g. GCN, ResGCN, GraphSAGE, and JKNet) for enhanced performance. Extensive experiments on several benchmarks verify that DropEdge consistently improves the performance on a variety of both shallow and deep GCNs. The effect of DropEdge on preventing over-smoothing is empirically visualized and validated as well. Codes are released on~\url{https://github.com/DropEdge/DropEdge}.
Representation learning methods that transform encoded data (e.g., diagnosis and drug codes) into continuous vector spaces (i.e., vector embeddings) are critical for the application of deep learning in healthcare. Initial work in this area explored the use of variants of the word2vec algorithm to learn embeddings for medical concepts from electronic health records or medical claims datasets. We propose learning embeddings for medical concepts by using graph-based representation learning methods on SNOMED-CT, a widely popular knowledge graph in the healthcare domain with numerous operational and research applications. Current work presents an empirical analysis of various embedding methods, including the evaluation of their performance on multiple tasks of biomedical relevance (node classification, link prediction, and patient state prediction). Our results show that concept embeddings derived from the SNOMED-CT knowledge graph significantly outperform state-of-the-art embeddings, showing 5-6x improvement in ``concept similarity" and 6-20\% improvement in patient diagnosis.